S = k/t where k is a constant, which two statements are correct?

a. [tex]123.1(1.069)^3 \approx 150.4[/tex]

b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]

Hence, the [tex]200th[/tex] term in the sequence is [tex]1613[/tex].

What is the sequence?

A sequence is a list of objects, typically numbers, in which order matters, repetition is allowed, and the same elements can appear multiple times at different positions in the sequence.

Here given that,

The sequence is

[tex]21,29,37,45,53,...[/tex]

The general formula is

[tex]a_n=a_1+d(n-1)[/tex]

[tex]a_1=21[/tex]

[tex]d=a_2-a_1\\d=29-21\\d=8[/tex]

Substitute it in the general formula is

[tex]a_2_0_0=21+8(200-1)\\a_2_0_0=21+8(199)\\a_2_0_0=21+1592\\a_2_0_0=1613[/tex]

Hence, the [tex]200th[/tex] term in the sequence is [tex]1613[/tex].

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Answer:

  A.  n ≥ 11

Step-by-step explanation:

You have a triangle with sides (n), (n-3), and 2(n-2). Its perimeter is at least 37 units, and you want to know the value of n.

The perimeter is the sum of the side lengths:

  P = (n) +(n -3) +2(n -2)

  P = n + n -3 +2n -4

  P = 4n -7

The perimeter is at least 37, so we have ...

  P ≥ 37

  4n -7 ≥ 37

  4n ≥ 44 . . . . . . . add 7

  n ≥ 11 . . . . . . . divide by 4

The value of n is at least 11.

Answer:

Step-by-step explanation:

You want to find the distance traveled by light in km for periods of 1–5 seconds at a speed of 299,792,458 m/s.

The speed is given in meters per second, and the table values are wanted in kilometers. There are 1000 meters in 1 km, so it can be convenient to convert the speed to km/s before doing other calculations.

  (299,792,458 m/s) / (1000 m/km) = 299,792.458 km/s

The distance is found by multiplying the speed by time:

  d = 299,792.458t

It is convenient to let a calculator do the multiplication (and rounding). The attachment shows the result of using t = {1, 2, 3, 4, 5}.

The distances are, respectively, {299792, 599585, 899377, 1199170, 1498962} km.

Answer:

---------------------------

It is assumed the first column represents x- values and the second column represents y- values.

Inverse variation equation:

Substitute one pair of coordinates, x = 3, y = 10:

Correct choice is B.

Answer:

b) k = 30

Step-by-step explanation:

Formula we use,

→ y = k/x

Now the value of k will be,

→ y = k/x

→ 10 = k/3 || → 6 = k/5

→ k/3 = 10 || → k/5 = 6

→ k = 10 × 3 || → k = 6 × 5

→ [ k = 30 ] || → [ k = 30 ]

Hence, the value of k is 30.

Aaron has to read 41 pages on the 6th day to reach his goal.

What is the speed of reading?

Any of the many methods that promise to increase one's reading speed include speed reading. Chunking is one speed-reading technique, as is reducing subvocalization. The many available speed-reading training programs may utilize books, videos, software, and seminars.

We have,

26 pages per day for 6 days:

26×6=156,

So Aaron should read 156 pages by the 6th day to reach his goal,

During the first 5 days, he reads 23 pages per day then,

23 × 5 = 115

That’s how many pages he’s already read.

156-115=41

Hence, Aaron has to read 41 pages on the 6th day to reach his goal.

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The values are;

⇒ F ∩ H = Ф

⇒ F ∪ H = (- ∞, 7]

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

F and H are defined as;

F = {v | v < 4 }

H = {v | v ≥ 7 }

Now,

Since, F and H are defined as;

F = {v | v < 4 }

H = {v | v ≥ 7 }

Hence, The values are;

F ∩ H = {v | v < 4 } ∩  {v | v ≥ 7 }

         = Ф

And, F ∪ H = {v | v < 4 } ∪  {v | v ≥ 7 }

                 = (- ∞, 7]

Thus, The values are;

⇒ F ∩ H = Ф

⇒ F ∪ H = (- ∞, 7]

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x under the assumption that x >0 x-70/x<-3, x > -35

WHAT IS INEQUALITY?

Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income (the quantity of money people get paid) (the amount of wealth people own). There are significant forms of economic inequality among various groups of people in addition to economic inequality between nations or states. Wealth, income, as well as consumption are the three main focuses of significant economic measurements. There are numerous ways to gauge economic inequality, with the Gini coefficient being among the most popular. The Disparities Human Development Index is a statistic composite index which offers another type of measurement by taking inequality into account.

assuming x > 0,

(x-70/x) < 3

= x-70 < 3x = -70 < 2x

= x > -35

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The correct comparison between the given numbers ; √160 and 115 / 9 is; 115 / 9 > √160.

It follows from the task content that the sign which correctly compares the two numbers as given in the task content be determined.

Since the given numbers in the task content can be evaluated as follows;

√160 = 12.64911064.

115 / 9 = 12.7777777778

From the results of the evaluations as represented above, since 12.7777777778 is greater than 12.64911064, it follows that the 115 / 9 > √160.

Therefore, the required correct comparison is;

115 / 9 > √160

The answer choice which is correct is as represented above.

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Two different data sets that have a median of 13 are

From the question, we have the following parameter

Median =13

The median of a dataset is the number at the middle position

So, we can make use of the following dataset

9, 10, 13, 18, 20

This is so because the middle number is 13

Another possible dataset is

10, 13, 13, 18

Similarly, this is because the middle number is 13

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The inverse function of g is g⁻¹(x) = √(x/2 +  1/2)

From the question, we have the following equations

f(x) = x - 2

g(x) = 2x² - 1

h(x) = 2x³ + 4

To determine the inverse function of g, we start by making the function f(x) as an equation

So, we have

y = 2x² - 1

Swap variables x and y

x = 2y² - 1

Add 2 to both sides

2y² = x +  1

Divide by 2

y² = x/2 +  1/2

Square root both sides

This gives

y = √(x/2 +  1/2)

So, we have

g⁻¹(x) = √(x/2 +  1/2)

Here, we have

f(x) = x - 2

h(x) = 2x³ + 4

This gives

f(h(x)) = h(x) - 2

So, we have

f(h(x)) = 2x³ + 4 - 2

Evaluate

f(h(x)) = 2x³ + 2

So, we have

f(h(x)) = 2(-2)³ + 2

Evaluate

f(h(x)) = -14

Here, we have

f(x) = x - 2

g(x) = 2x² - 1

This gives

g(f(x)) = 2(f(x))² - 1

So, we have

g(f(x)) = 2(x - 2)² - 1

So, we have

g(f(5)) = 2(5 - 2)² - 1

Evaluate

g(f(5)) = 17

Hence, the functions g(f(5)) is 17

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Answer:

a) g^-1(x) = - √2x+1, √2x+1

                        2         2

b) -14

c) 17

Step-by-step explanation:

a) g(x) = 2x² - 1

y= 2x² - 1 becomes x = 2y² - 1

Solve for y: x = 2y² - 1

g^-1(x) = - √2x+1, √2x+1

                    2         2

*answer is: -√2x+1 (over) 2 & √2x+1 (over) 2*

b) Find: f(h(-2))

h(x) = 2x³ +4

h(-2) = 2(-2)³ + 4

= - 12

f(x) = x – 2

f(-12) = (-12) – 2

= -14

c) Find: g(f(5))

f(x) = x – 2

f(5) = (5) – 2

= 3

g(x) = 2x² - 1

g(3) = 2(3)² - 1

= 17

The volume for the largest box will be 1.056 foot³. This can find out by application of differentiation.

What is AOD?

AOD is nothing but application of differentiation. It implies scopes where we can use differentiation to make our calculations easy.

Here, given

Length and breadth = 2,3 foot

Let us consider length of side of square = x

So, after cutting squares left sides of rectangular sheet = 2-2x , 3-2x

So, volume = (2-2x)*(3-2x)*x

                v = 4x³ - 10x² + 6x

To find largest volume , [tex]\frac{dv}{dx}[/tex] = 0

                 [tex]\frac{dv}{dx}[/tex] = 12x² - 20x + 6

                12x² - 20x + 6 = 0

                x = 0.4 , 1.3

But, for 1.3 volume will be negative i.e. not possible.

So, volume = 2.2*1.2*0.4

                   = 1.056 foot³

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Answer:Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.

If mean of 11 numbers is 7 one of the numbers, 13, is deleted then the mean of remaining 10 numbers is 6.4

The mean of 7 numbers = 11

We know,

Mean = Sum of the terms / Number of terms

Substitute the values in the equation

11 = Sum of the terms / 7

The sum of the terms = 11 × 7

= 77

Number 13 is deleted

Sum of the terms = 77 - 13

= 64

Number of terms = 11 - 1

= 10

The mean = Sum of the terms / Number of terms

Substitute the values in the equation

= 64 / 10

= 6.4

Hence, the mean of the remaining 10 numbers is 6.4

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Answer: it would be 18 candies that are left

Step-by-step explanation:  

I did the math

c=1/2  which makes fx|y (x, y) a valid conditional probability mass function.

What is conditional probability?

The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is determined by multiplying the likelihood of the earlier event by the increased likelihood of the later, or conditional, event.

Given that;

p(x) = [tex]c (\frac{2}{3} )^n[/tex]   where x = 1,2,3,........

for getting value of c we are using the expression :

[tex]\sum_{n=1}^{\infty} c(\frac{2}{3})^n = 1[/tex]

[tex]c\sum_{n=1}^{\infty} (\frac{2}{3})^n = 1[/tex]

Since we want p(x) to be a Probability Mass Function, your approach is correct, since for any such function

fX:A→[0,1],X:S→A⊆R, it is :

[tex]\sum _{x\in A} \ fX(x)=1[/tex]

As long as you've correctly understood that condition, you can proceed with your specific exercise as follows:

[tex]\sum_{n=1}^{\infty} c(\frac{2}{3})^n = 1[/tex]

⇔ [tex]c\sum_{n=1}^{\infty} (\frac{2}{3})^n = 1[/tex]

⇔2c = 1

⇔c = 1/2

Hence c =  1/2 is the valid conditional probability mass function.

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Answer:

0.13, 0.16, 0.19, 0.22

Step-by-step explanation:

You are adding 0.03 each time

Answer:

0.13, 0.16, 0.19, 0.22

Step-by-step explanation:

Add 0.03 to each.

The x- and y-coordinates of the center of mass are; (20, 0)

The center of mass is the location where the sum of the relative position of the masses in a mass distribution is zero. It is the point where force can be applied on the distributed mass without causing a rotation of the system.

The mas of the steel plate = 800 g = 0.8 kg

The base length of the isosceles triangular plate = 20 cm = 0.2 m

The height of the isosceles triangular plate = 30 cm = 0.3 m

Considering a small strip of height, dx and width, I, we get

Area of small strip, dA = I·dx

Density of the plate for a unit thickness, ρ = M/A

Density of the small strip of mass dm = dm/dA

Considering the density of the plate as uniform, we get;

[tex]\displaystyle {\frac{dm}{dA} =\frac{M}{A}[/tex]

Therefore;

[tex]\displaystyle {dm=\frac{M}{A}\times dA}[/tex]

The area of the triangular plate, A = (1/2) × 0.2 m × 0.3 m = 0.03 m²

Mass of the plate, M = 0.8 kg

Therefore;

[tex]\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx}[/tex]

The width of the small strip, I, located at a distance x from the vertex of the triangular plate, using similar triangles, indicates;

[tex]\dfrac{I}{20} = \dfrac{x}{30}[/tex]

[tex]I=20\times \dfrac{x}{30} = \dfrac{2}{3} \cdot x[/tex]

Therefore;

[tex]\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx} = \frac{0.8}{0.03}\times \dfrac{2}{3} \cdot x\cdot dx}[/tex]

The center of mass, [tex]x_{cm}[/tex], can be obtained with the formula; [tex]\displaystyle {x_{cm} = \dfrac{1}{M} \cdot \int\limits {x} \, dm }[/tex]

Therefore; [tex]\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx }[/tex]

[tex]\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx } = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx[/tex]

[tex]\displaystyle {x_{cm} = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0[/tex]

[tex]\displaystyle {x_{cm} = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0=\frac{200}{9} \times \frac{0.027}{3} =0.2[/tex]

The location of the x-coordinate center of mass, [tex]x_{cm}[/tex] = 0.2 m = 20 cm from the vertex, which is the same location as the x-coordinate of the centroid of the plate of uniform density.

The plate is symmetrical about the x-axis, therefore, the y-coordinate of the center of mass is along the x-axis, which is [tex]y_{cm}[/tex] = 0

The coordinate of the center of mass = (0.2, 0)

Part of the question requires the location of the coordinate of the center of mass of the triangular plate

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Answer:

answers attached int he files below all in order

The probability that the sample mean would be less than 43.4 dollars is 0.9292.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.

From the information, the mean cost of a five pound bag of shrimp is 42 dollars with a variance of 49 and a sample of 54 bags of shrimp is randomly selected.

Therefore, the probability will be:

P(x < 43.4)

Using normal distribution

= P(z < 43.4 - Mean( / 7/✓54)

= P(z < 43.4 - 42( / 7/✓54)

= P(z < 1.4697)

= 0.9292

The probability is 0.9292.

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The expression  -3/10 X (-8/15) is positive

Expression

Expression in mathematics has two or more variables, terms and constants. Also, arithmetic expression contains only numbers and mathematical operators and algebraic expression

The expression has negative sign and from mathematical calculation we already know the following relation:

+ x + = +

positive multiply by positive equals Positive

- x - = +

Negative multiply by Negative equals Positive

+ x - = -

Positive multiply by Negative equal Negative

hence,   - [tex]\frac{3}{10}[/tex] x - [tex]\frac{8}{15}[/tex]

The negative sign multiply by  -3/10 X (-8/15) sign will give positive.

Therefore, the expression  -3/10 X (-8/15) is positive.

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Answer:

4

Step-by-step explanation:

(8+2-4)+(3-5)

(10-4)+(-2)

6-2

4

Hopes this helps please mark brainliest

The difference in b-tree and b +tree, b -tree is a self balancing tree data structure that maintains sorted data and b +tree is a modified version of b -tree.

b -tree is used to sort the data with various pieces facilities such as insertion ,deletion and search etc  whereas b +tree is a modified version of b -tree providing all the functions smoothly and quickly .

In b -tree, both internal nodes and leaf nodes are used to store records and keys whereas in b +tree keys are stored in internal nodes whereas records are storing leaf nodes

In b +tree, no duplication is allowed but in b +tree duplication may occur

A b +tree usually preferred as an access structure to a data file as as the height of the tree remains balanced and less as compared to b -tree . We can assess the data stored in b +tree sequentially as well as directly . keys are used for indexing . Faster search queries as the data is stored only on a leaf nodes.

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Answer:

8+8-8×1

8+8-8

16-8

8 Ans.

The quadratic function, f(x) = 3·x² + 6·x, has the following values;

1. The function has a minimum value

2. The y-intercept of the function is (0, 0)

The axis of symmetry is; x = -1

The x-coordinate of the vertex is; x = -1

3. The table of values can be presented as follows;

x   [tex]{}[/tex]-2    -1    0

f(x) [tex]{}[/tex]0    -3     0

The vertex is (-1, -3)

4. Please find attached the graph of the function

A quadratic function is a function that has 2 as the highest power of the variables.

The specified function is; f(x) = 3·x² + 6·x

1. The coefficient of x² in the specified  quadratic function, which indicates the existence of a minimum or maximum value is positive, therefore, the function has a minimum value

2. The y-intercept is the value of the function when x = 0, therefore;

f(0) = 3 × 0² + 6 × 0 = 0

Therefore, at the y-intercept, x = 0, and f(x) = 0

The y-intercept is (0, 0)

The axis of symmetry is a line that passes through the vertex

A the vertex, we get, f'(x) = 6·x + 6 = 0

Therefore;  6·x + 6 = 0

6·x = -6

x = -6/6 = -1

f(-1) = 3·(-1)² + 6 × (-1) = -3

The vertex is (-1, -3)

Therefore, the  axis of symmetry is the line x = -1

The x-coordinate of the vertex of the function is; x = -1

3. A table of values for the function can be presented as follows;

x    [tex]{}[/tex]           f(x)

-6    [tex]{}[/tex]           72

-5     [tex]{}[/tex]          45

-4     [tex]{}[/tex]          24

-3    [tex]{}[/tex]           9

-2    [tex]{}[/tex]           0

-1    [tex]{}[/tex]           -3

0    [tex]{}[/tex]           0

1    [tex]{}[/tex]            9

2     [tex]{}[/tex]           24

3    [tex]{}[/tex]            45

4    [tex]{}[/tex]            72

5    [tex]{}[/tex]             105

4. . Please find attached the graph of the function created with MS Excel

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The probability that you take different colors in two"picks" is 31/45.

You could choose one red followed by one blue, one blue followed by one red, one blue followed by one black, one black followed by one blue, one black followed by one red, or one red followed by one black.

P( different colors) = P( one blue followed by one red ) +P( one red followed by one blue) + P( one blue followed by one black ) +P( one black followed by one blue) +P( one black followed by one red ) +P( one red followed by one black)

P(one blue followed by one red) = (10/20)( 6/19) = 3/19

P(one red followed by one blue) = (6/20)( 10/19) = 3/19

P(one blue followed by one black) = (10/20)( 4/19) = 2/19

P(one black followed by one blue) = (4/20)( 10/19) = 2/19

P(one red followed by one black) = (6/20)( 4/19) = 6/95

P(one black followed by one red) = (4/20)( 6/19) = 6/95

P(different colors )= 3/19 + 3/19 + 2/19 + 2/19 + 6/95 + 6/95
                                = 31/45

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The solution for x in the inequality expression is x < -8

From the question, we have the following inequality expression that can be used in our computation:

-4x+5>37

Subtract 5 from both sides of the inequality

So, we have

-4x + 5 - 5 >37 - 5

Evaluate the like terms

This gives

-4x > 32

Divide both sides by -4

x < -8

Hence, the solution is x < -8

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In 2000, cable was available in 45683700000 homes.

Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.

In 1980, 17700000 = 25.8%\s1% = 4566600000

Then, in 2000, there were 45683700000 households (17 700 000 + 4566 600 000).

Comparing two amounts while rebasing the second amount to 100 is the simplest way to use percentages. Let's assume that we are interested in the proportion of employed women who are female.

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The cost per ounce in both options is the same. Then the correct option is D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The rate is the ratio of the amount of something to the unit.

Jorge wants to buy a drink.

Choice 1: 24-ounce cup for $1.92

Choice 2: 12-ounce cups for $0.96 each

The cost per ounce in choice 1 is calculated as,

⇒ $1.92 / 24

⇒ $0.08 per ounce

The cost per ounce in choice 2 is calculated as,

⇒ $0.96 / 12

⇒ $0.08 per ounce

The cost per ounce in both options is the same. Then the correct option is D.

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