Prove 2n > n2. Decide for what integers n,the inequality is true. Use math induction to prove.
By substituting in n = 0, 1, 2... n (greater than or = to) 5 theequality is true.
1. Verify the basis.
Image for Prove 2^n > n^2. Decide for what integers n,the inequality is true. Use math induction to prove. By substituso 32 > 25.
So, P5 is true.
2. The Induction Step is where I need some help.
We can assume P_k is true for any n >= 5, which isImage for Prove 2^n > n^2. Decide for what integers n,the inequality is true. Use math induction to prove. By substitufor any k >= 5.
Need to show thatImage for Prove 2^n > n^2. Decide for what integers n,the inequality is true. Use math induction to prove. By substitu[This is where I'm stuck]

A possible equation that relates distance from home (d) and the amount of time (t) is d = tx, which can be expressed as 90= 3x.

An equation relates variables using the equality symbol (=) as well as other symbols such as addition or subtraction. Due to this follow these steps:

Based on this a possible equation is:  d = tx

The missing value can be found by solving the equation 90= 3x.

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Answer:

need point Ibut nadir me ayuda y la app no me deja seguir

Answer: $22

Step-by-step explanation:

Answer:

Step-by-step explanation:f (4) f (4) Use the slope-intercept form to find the slope and y-intercept. Slope: 4 4 y-intercept: (0,0) (0, 0) Any line can be graphed using two points. Select two x x values, and plug them into the equation to find the corresponding y y values.

Answer:

3x+ 5 is a factor

Step-by-step explanation:

  9x² + 21x + 10

Sum = 21

Product = 90

Factors = 15 * 6    {15*6=90  & 15+6 = 21}            

9x² + 21x + 10 = 9x² + 15x + 6x + 10

              {Rewrite the middle term using factors}

                       = 3x(3x + 5) + 2(3x + 5)

                       = (3x + 5)(3x + 2)

3x + 5 is a factor.

By using the natural logarithm, we can see that the solution is x = 2.26.

Here we want to solve the equation below:

2²ˣ = 23

If we apply the natural logarithm in both sides, we will get:

ln(2²ˣ) = ln(23)

That allows us to bring down the exponent:

ln(2²ˣ) = ln(23)

2x*ln(2)  =ln(23)

x = ln(23)/(2*ln(2))

x = 2.26

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The value of exponential function f (4) is 1,296.

The value of the exponential function is obtained from the common ratio of the resultant value of the number.

f ( 2 ) = 36

f ( 3 ) = 216

common ratio = ( f (3) ) / ( f (2) )

common ratio =  ( 216 ) / ( 36 )

common ratio = 6

so, f (2) = 6² = 36

f (3) = 6³ = 216

The value of exponential function f (4) is calculated as follows

Now, f (4) = 6⁴ = 1,296

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In this question the volume and the height is given.

But we need to find the height of the cylinder

In order to find the height we use the volume of a cylinder formula,

212 =  πr²h

Applying the given values in a equation we get

[tex]212[/tex] = [tex]\frac{22}{7} X(3)^{2} X h[/tex]

[tex]212 = \frac{22}{7} X 9[/tex][tex]X h[/tex]

[tex]7.5 = h[/tex]

Answer:

2.50

Step-by-step explanation:

The marginal revenue when output rises from 310 to 370 pounds is $1.75 per pound.

Given that a table containing Total Output (Q), Price per Pound ($1.50), Total Revenue we need to find the marginal Revenue when output rises from 310 to 370 pounds.

To calculate marginal revenue, we need to determine the change in total revenue when output increases from 310 to 370 pounds.

Total revenue at 310 pounds = $555.00

Total revenue at 370 pounds = $660.00

Change in total revenue = $660.00 - $555.00 = $105.00

Since the change in total revenue is $105.00 and the change in output is 60 pounds, we can calculate marginal revenue as:

Marginal Revenue = Change in Total Revenue / Change in Output

= $105.00 / 60 pounds

= $1.75 per pound

Hence the marginal revenue when output rises from 310 to 370 pounds is $1.75 per pound.

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The increased number of tickets will be 220.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the number of tickets is increased by a factor of 1.1. The increased amount will be calculated as:-

Amount = 200 x 1.1

Amount = 220

Hence, the increased number of tickets will be 220.

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The small upper quartile is 81.

A random sample of 60 fourth graders are selected.

Since, there are 60 values.

The median of a set of data is the middlemost number or center value in the set. The median is also the number that is halfway into the set.

Sample median will be Average of [tex](\frac{60}{2} )^{th}[/tex] value and [tex](\frac{60}{2}+1)^{th}[/tex] value

The formula to calculate the median of the finite number of data set is given here. The median formula is different for even and odd numbers of observations. Therefore, it is necessary to identify first if we have odd number of values or even number of values in a given data set.

If the total number of observations given is odd, then the formula to calculate the median is:

If the total number of observation is even, then the median formula is:

Sample median = Average of 30th value and 31st value

From the stem and leaf plot :

30th value = 81

31st value = 81

Sample median = (81+81)/2 = 81

Therefore, the sample upper quartile is 81.

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The mean of data set A is greater than the mean of data set B i.e. D.

What is mean?

The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.

z-score is a statistical measurement that describes a value's relationship to the mean of a group of values and the formula for the z-score is

z = (x - μ)/σ

x = data point

μ = mean

σ = standard deviation

Now,

Given Data sets

Data Set A: 1, 2, 3, 4, 5, 6, 7

Data Set B: 1, 1, 2, 2, 3, 3, 4

For Data Set A

Mean=(1+2+3+4+5+6+7)/7=28/7=4

For Data Set B

Mean=(1+1+2+2+3+3+4)/7=16/7=2.28

Hence,

          The mean of data set A is greater than the mean of data set B.

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Answer: [tex]y=4x+50[/tex]

Step-by-step explanation:

The probability that the maximum of the two dice is greater than or equal to six is; 0.722

For any two dice being rolled, the sample space for total number of possibilities is 36.

Now, the combination that will result in a sum greater than or equal to 6 are as follows;

(1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6), (4, 2), (4, 3), (4, 4),(4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

Thus, the probability is;

P(MAX Sum≥ 6) = 26/36

= 0.722

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Answer:

OOk

Step-by-step explanation:

Answer:

[tex]h \:(x) = 30 \: {x}^{2} - 54x + 10[/tex]

Answer:

6.

Step-by-step explanation:

1. FH is diameter, then

2. m(∠FGH)=90°, but

3. from other side m(∠FGH)=16x-6, then it is possible to write:

16x-6=90; ⇒ x=6.

4. finally, answer is 6.

Therefore , the solution of the given problem of expression comes out to be  [tex]\frac{1}{2} \times(5x-3)^{\frac{1}{4}}[/tex] is the left expression.

Mathematical operations including addition, subtraction, multiplication, and division are required. They result in the following when combined: An equation, some information, and an arithmetic operator Values, parameters, and operations like adds, omissions, multiplications, and divisions make up a statement of fact. Different phrases and words can be contrasted and compared.

Here,

Given :

=>[tex](5x - 3)^\frac{1}{4} - 1/2(5x-3)^\frac{1}{4}[/tex]

=> [tex](5x-3)^{1/4} {1-\frac{1}{2 }[/tex]

=>[tex](5x -3)^\frac{1}{4} \times \frac{1}{2}[/tex]

=> [tex]\frac{1}{2} \times(5x-3)^{\frac{1}{4}}[/tex]

Thus , answer is [tex]\frac{1}{2} \times(5x-3)^{\frac{1}{4}}[/tex]

Therefore , the solution of the given problem of expression comes out to be  [tex]\frac{1}{2} \times(5x-3)^{\frac{1}{4}}[/tex] is the left expression.

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Answer:

see attached

Step-by-step explanation:

intercept on Y is when x=0, y = 16 so if no one goes to competition A, they'll have 16 six-member teams

intercept on x is when y=0, x=24 so if no one goes to competition B, they'll have 24 four-member teams

The expected number of offspring, given the probabilities of offspring is   1. 64 offspring.

To find the expected number of offspring to the healthy adult female, look at the probability of an offspring and the number of offspring.

Multiply these probabilities with the offspring and then sum up the quotients.

The expected number of offspring is therefore:

= ( 0 x 30 %) + ( 1 x 0.22 ) + ( 2 x 0.17 ) + ( 3 x 0. 16 ) + ( 4 x 0.15)

= 1. 64 offspring

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On solving the provided question we can say that equation of new line is y + 2 = -1/3(4x + 2)

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

lines,

y - 1 = -3(x-2)

3y = x- 9

here slope, m is -3

equation of new line is

y + 2 = -1/3(4x + 2)

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The quantity of square yards of carpeting that Maxie needs would be = 8 square yards.

The area of the room in square feet = 72 ft²

The carpeting is sold in the measurement of = square yard.

But, 1 square yard = 9 square feet.

Therefore the conversation of 72 ft² to yards²;

= 1 yard² = 9 ft²

X yard² = 72 ft²

Make X the subject of formula;

X= 72/9

X= 8 square yards.

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a) At the instant when the radius of the oil slick is 100 centimeters and the height is 0.5 centimeters, the volume of the oil slick is given by V = πr^2h = π(100^2)(0.5) = 50,000π cubic centimeters.

Since the volume of the oil slick is increasing at the constant rate of 2000 cubic centimeters per minute, the rate of change of the height with respect to time can be found using the equation:

dV/dt = 2πrh dr/dt + 2πr^2 dh/dt

Setting r = 100 cm, h = 0.5 cm, dr/dt = 2.5 cm/min, and dV/dt = 2000 cm^3/min, we get:

2000 = 2π(100)(0.5) dr/dt + 2π(100^2) dh/dt

Solving for dh/dt, we get:

dh/dt = (2000 - 2π(100)(0.5) dr/dt)/(2π(100^2)) = (2000 - 500π dr/dt)/(200π)

Substituting dr/dt = 2.5 cm/min, we get:

dh/dt = (2000 - 500π * 2.5)/(200π) = (2000 - 1250)/200π = (850 - 1250)/200π = -400/200π cm/min

So, the rate of change of the height of the oil slick with respect to time at this instant is -0.63 cm/min.

b) Let t be the time elapsed since the recovery device began working. The volume of the oil slick at time t is given by:

V(t) = πr^2(h) = π(100^2 + 2.5t)^2(0.5 + 0.63t)

Since the rate of oil removed by the recovery device is R(t) = 400V(t) cubic centimeters per minute, the rate of change of the volume of the oil slick with respect to time is:

dV/dt = 2πr dr/dt h + 2πr^2 dh/dt - 400V(t)

Setting r = 100 + 2.5t, h = 0.5 + 0.63t, dr/dt = 2.5 cm/min, and dh/dt = 0.63 cm/min, and substituting into the equation, we get:

dV/dt = 2π(100 + 2.5t)(2.5) (0.5 + 0.63t) + 2π(100 + 2.5t)^2(0.63) - 400π(100 + 2.5t)^2(0.5 + 0.63t)

Since dV/dt = 2000 - 400V(t), we get:

2000 = 2π(100 + 2.5t)(2.5) (0.5 + 0.63t) + 2π(100 + 2.5t)^2(0.63) - 400π(100 + 2.5t)^2(0.5 + 0.63t) + 400V(t)

This is a nonlinear differential equation that can be solved using numerical methods to find the time when the oil slick reaches its maximum volume. The exact time when the oil slick reaches its maximum volume cannot be determined analytically.

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Answer:

115.7625

Step-by-step explanation:

100(1.05)^3=115.7625

The correct option in the given situation is (C) there are twice as many terms in sequence y as there are in sequence x.

A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important.

Similar to a set, it has members (also called elements, or terms).

The length of the series is the number of elements (potentially infinite).

In contrast to a set, the same items might appear more than once in a sequence at various points, and unlike a set, the order is important.

A sequence can be described formally as a function from natural numbers (the positions of the sequence's elements) to the items at each of those positions.

An indexed family, which is a function from any index set, can be thought of as a generalization of the idea of a sequence.

So, we have:

x: begin at 2, add 3 = 5

y: begin at 4, add 6 = 10

According to the given statements, the best statement going with the situation is (C) the terms in sequence y are two times the terms in sequence x.

Therefore, the correct option in the given situation is (C) there are twice as many terms in sequence y as there are in sequence x.

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Answer:
it took Sean 3 hours to write the essay.

Step-by-step explanation:

We know that the ratio of time Sean spent writing the essay to the time he spent revising the essay was 4:1, which means that for every 4 units of time he spent writing the essay, he spent 1 unit of time revising it.

Let's call the time he spent writing the essay "x" and the time he spent revising the essay "y". We know that x + y = 15 (because he spent a total time of 15 hours writing and revising the essay) and that the ratio of x to y is 4:1, so 4x = y.

We can substitute the second equation into the first equation:

x + 4x = 15

5x = 15

x = 3

So it took Sean 3 hours to write the essay.

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Answer: the store offered an 18.75% discount on the car

Step-by-step explanation:

According to the given time card the pay for the day is $96.25.

To calculate the pay for a day, we need to determine the total number of hours worked for that day. We can do this by subtracting the start time from the end time for each shift.

In the morning, the start time is 8:00 and the end time is 12:00, so the number of hours worked is 12:00 - 8:00 = 4 hours.

In the afternoon, the start time is 12:45 and the end time is 17:30, so the number of hours worked is 17:30 - 12:45 = 4 hours and 45 minutes, which we can convert to decimal form by dividing 45 by 60 to get 0.75 hours.

The total number of hours worked is 4 + 4.75 = 8.75 hours.

Since the wage is $11/hr, the pay for the day is 8.75 hours * $11/hr = $96.25.

Rounding to the nearest hundredth, the pay for the day is $96.25.

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The equation of the line passing through (2, 3) and (-1, -1). is 3y = 4x + 1

An equation is an expression that shows how two or more numbers and variables are related to each other. Types of equations can either be linear, quadratic or cubic

The standard form of a linear equation is:

Ax + By = C

Where A, B and C are constants

The slope intercept form of a linear function is:

y = mx + c

m is the rate of change and b is the y intercept

The graph passes through (2, 3) and (-1, -1). Hence:

y - 3 = [(-1-3)/(-1-2)] (x - 2)

y - 3 = (4/3)(x - 2)

multiply through by 3:

3y - 9 = 4(x - 2)

3y - 9 = 4x - 8

3y = 4x + 1

The equation of the line is 3y = 4x + 1

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