hich of the these are steps for a proof by mathematical induction that P(n) is true for all positive integers n? a. Verify that P(1) is true. b. Demonstrate that the conditional statement Plk) implies Plk+1) is true for all positive integers k. c. Verify that P(1), P(2), P(3), ..., P(k) are all true, where k is a specific large, positive integer. d. Demonstrate that if P(k) is false, then Plk+1) is false for all positive integers k. e. Demonstrate that P(k+1) implies plk) is true for all integers k.

Answer:

The sequence is defined as follows:

a1 = 5

an = an-1 - 5, for n > 1

Using this definition, we can find the first four terms of the sequence as follows:

a1 = 5

a2 = a1 - 5 = 5 - 5 = 0

a3 = a2 - 5 = 0 - 5 = -5

a4 = a3 - 5 = -5 - 5 = -10

Therefore, the first four terms of the sequence are: 5, 0, -5, -10.

The equation that correctly represents this situation is c(t) = 45 + 45(t-2). This equation states that the total number of credits the student will have after t semesters is equal to 45 (the number of credits they had before beginning college) plus 45 times the number of semesters after two (t-2).

To explain this equation in more detail, we need to break it down. First, the student had some credits earned while in high school, so the equation starts off with c(t) = 45, which is the number of credits the student had before beginning college.

Next, 45(t-2) represents the number of credits earned in the additional semesters since college began. The t-2 part of the equation means that the total number of credits earned in the additional semesters starts at zero for t = 2. Then, for each additional semester, 45 credits are added. So, for example, when t = 5, 45 credits are added to the initial 45 credits the student had before beginning college, resulting in 90 credits.Therefore, the equation  c(t) = 45 + 45(t-2)  correctly represents this situation.

To know more about derivation, click here:

https://brainly.com/question/23847661

#SPJ11

the variance of X is 9. b) Determine E [2X² - 20X +5]:

Using linearity of expectation, we can find E [2X² - 20X +5] as:

E [2X² - 20X +5] = 2E[X²] - 20E[X] + 5

by the question.

The number of ways to select the first 2 white chips is given by:

Number of ways = (6C2) (5C0) (3C0) = 15

The number of ways to select the third chip as blue given that the first 2 chips were white is given by:

Number of ways = (3C1) = 3

Therefore, the probability of selecting the third chip as blue given that the first 2 chips were white is:

P(The third chip is blue the first 2 were white) = Number of ways / Total number of ways = 3 / 350 = 0.0086 (rounded to 4 decimal places)

c) P(The fourth chip is blue the first 2 were white):

The number of ways to select the first 2 white chips is given by:

Number of ways = (6C2) (5C0) (3C0) = 15

The number of ways to select the third chip as non-white given that the first 2 chips were white is given by:

Number of ways = (8C1) = 8

The number of ways to select the fourth chip as blue given that the first 2 chips were white, and the third chip was non-white is given by:

Number of ways = (3C1) = 3

Therefore, the probability of selecting the fourth chip as blue given that the first 2 chips were white is:

P(The fourth chip is blue the first 2 were white) = Number of ways / Total number of ways = 8*3 / 350 = 0.0686 (rounded to 4 decimal places)

Suppose we have a random variable X such that E[X]= 7 and E[X²] =58.

a) Determine the variance of X:

The variance of X is given by:

Var[X] = E[X²] - (E[X]) ²

Substituting the given values, we get:

Var[X] = 58 - (7) ² = 9

To learn more about random variable:

https://brainly.com/question/17238189

#SPJ

Thus, a 0.1271 area under the standard normal curve corresponds to a z-score of roughly -1.14.

The degree of variance or dispersion in a set of data values is measured by standard deviation. It computes the deviation of each data point from the mean (average) of the data. While a high standard deviation suggests that the data points are dispersed throughout a broader range of values, a low standard deviation suggests that the data points tend to be close to the mean. In statistics, the standard deviation is frequently used to evaluate the level of variability or dispersion within a data collection.

given

Using a normal distribution function on a calculator or a standard normal distribution table, we can determine the z-score that corresponds to an area of 0.1271 under the standard normal curve.

We can enter the following data into a calculator equipped with a normal distribution function:

Area = 0.1271

Mean = 0 (because we are using the usual normal distribution) (since we are using the standard normal distribution)

Standard deviation equals one (since we are using the standard normal distribution)

Calculating this, we obtain:

Z is equal to invNorm(0.1271, 0, 1) = -1.14.

Thus, a 0.1271 area under the standard normal curve corresponds to a z-score of roughly -1.14.

To know more about standard deviation visit:

https://brainly.com/question/23907081

#SPJ1

Answer:

it is -1.14

Step-by-step explanation:

I took the k12 quiz

The first 4 terms of the sequence represented by the expression 3n + 5

is 8, 11, 14 and 17.

Sequence:

In mathematics, an array is an enumerated collection of objects in which repetition is allowed and in case order. Like a collection, it contains members (also called elements or items). The number of elements (possibly infinite) is called the length of the array. Unlike sets, the same element can appear multiple times at different positions in the sequence, and unlike sets, order matters. Formally, a sequence can be defined in terms of the natural numbers (positions of elements in the sequence) and the elements at each position. The concept of series can be generalized as a family of indices, defined in terms of any set of indices.

According to the Question:

Given, aₙ = (3n+5).

First four terms can be obtained by putting n=1,2,3,4

a 1=(3×1+5) = 8

a 2 =(3×2+5) = 11

a 3 =(3×3+5) = 14

a 4 =(3×4+5) = 17

First 4 terms in the sequence are 8, 11, 14, 17.

Learn more about Sequence:

https://brainly.com/question/30262438

#SPJ4

Answer:

Step-by-step explanation:

1. add 14 to 24

2. ur done!

Answer: The median is 6

Step-by-step explanation: The median is the data value separating the upper half of a data set from the lower half.

Arrange data values from lowest to highest value

The median is the data value in the middle of the set

If there are 2 data values in the middle the median is the mean of those 2 values.

Answer:

  -10/11

Step-by-step explanation:

You want the average rate of change of f(x) on the interval [-6, 5].

The average rate of change of function f(x) on the interval [a, b] is ...

  AROC = (f(b) -f(a))/(b -a)

  = (f(5) -f(-6))/(5 -(-6))

  = (-20 -(-10))/5 +6 = (-20 +10)/(5 +6)

  AROC = -10/11

The average rate of change on the interval is -10/11.

Answer:

I zont know i need points

Step-by-step explanation:

Yea im srry

The set of all possible y-values for the function h constitutes its range. The range is therefore [-3, 0].

The collection of all feasible output values (dependent variable) of a function is known as the range in mathematics. It is the totality of all possible numbers that the function can accept as input (an independent variable) and output. On the number line, the range is frequently represented by an interval or group of intervals. For instance, the range can be written as [-3, 3] if the domain of a function f(x) is [-2, 2] and its output numbers fall within [-3, 3].

given

The collection of all x-values for which h(x) is specified is the domain of the function h.

The graph's [-2, 4] domain can be determined by looking at the graph, which shows that it begins at x=-2 and concludes at x=4.

The set of all possible y-values for the function h constitutes its range. Looking at the graph, we can see that it takes all values between y=-3 and y=0, and that it begins at y=-3.

The range is therefore [-3, 0].

To know more about range visit:

https://brainly.com/question/28135761

#SPJ1

The complete question is :-  The entire graph of the function h is shown in the figure below. Write the domain and range of h as intervals or unions of intervals.

-2

-3-

4-

domain =

range =

a) Graph this system of inequalities, we can plot the lines x = 0, y = 0, x = 260, y = 320, and x + y = 380

b) The maximum profit of $5200 achieved.

Selling profit is the profit that a business makes on the sale of its products or services. It is the difference between the selling price and the cost of product.

a) Let x be the number of boards of mahogany sold and y be the number of boards of black walnut sold. Then, the constraints of the problem can be represented by the following system of inequalities:

x ≥ 0 (non-negative constraint)

y ≥ 0 (non-negative constraint)

x ≤ 260 (maximum number of mahogany boards available)

y ≤ 320 (maximum number of black walnut boards available)

x + y ≤ 380 (maximum number of boards that can be sold)

To graph this system of inequalities, we can plot the lines x = 0, y = 0, x = 260, y = 320, and x + y = 380 on a coordinate plane and shade the feasible region that satisfies all of the constraints. The feasible region is the area that is bounded by these lines and includes the origin (0, 0).

b) The profit function P(x, y) can be defined as follows:

P(x, y) = 20x + 6y

To maximize the profit, we need to find the values of x and y that satisfy all of the constraints and maximize the profit function P(x, y).

One way to do this is to use the corner-point method. We can evaluate the profit function at each of the corners of the feasible region and find the corner that gives the maximum profit.

The corners of the feasible region are (0, 0), (0, 320), (260, 0), and (120, 260).

P(0, 0) = 0

P(0, 320) = 6(320) = 1920

P(260, 0) = 20(260) = 5200

P(120, 260) = 20(120) + 6(260) = 4720

Therefore, the maximum profit of $5200 can be achieved by selling 260 boards of mahogany and 0 boards of black walnut.

To know more about inequalities, visit:

https://brainly.com/question/30238989

#SPJ1

Answer:

Step-by-step explanation:

Regular price:$19

60 per cent of $19 is 11.4 dollars.

but if ypu are looking for how much did she pay then it is..

19-11.4=$7.6

The rounding of the number to 1 significant figure is-

216 × 876 = 180000

216 × 876

This number can be written in form of rounding to 1 significant figure as;

200 × 900 = 180000

To know more about the significant figure, here

https://brainly.com/question/293578

Rs 5.25 can be expressed without decimals as Rs 525/100 or as 5 1/4 (or 5 ¼) using mixed numbers. Both methods allow us to represent the value of Rs 5.25 accurately without using decimal notation.

To express Rs 5.25 without using decimals, we need to convert it into a fraction with a numerator and a denominator. One way to do this is by multiplying both the numerator and the denominator by 100 to eliminate the decimal point.

So, Rs 5.25 can be written as Rs 525/100. This is also known as a fraction in its simplest form, as both the numerator and denominator have no common factors other than 1.

Another way to express Rs 5.25 without decimals is to use mixed numbers. A mixed number is a whole number combined with a fraction. To convert a decimal to a mixed number, we need to find the whole number part and the fraction part.

To find the whole number part, we can simply drop the decimal point and write the digits to the left of it. In this case, the whole number part is 5.

To find the fraction part, we need to subtract the whole number part from the original number and simplify the fraction. In this case, Rs 5.25 can be written as 5 and 1/4 (or 5 ¼), where the fraction part is 1/4.

In conclusion, Rs 5.25 can be expressed without decimals as Rs 525/100 or as 5 1/4 (or 5 ¼) using mixed numbers. Both methods allow us to represent the value of Rs 5.25 accurately without using decimal notation.

To know more about  mixed numbers. click here:

brainly.com/question/24137171

#SPJ4

Answer:

(-∝, 0)

Step-by-step explanation

f(x) will extend from negative infinity and approach but never reach the point where x = 0.

So the solution is  x > -infinity and < 0.

Answer:

15

Step-by-step explanation:

Answer can only be found through estimation.

This means you have to do:

[tex]\frac{50*3}{\sqrt{100} }[/tex]

This will get you 15.

The length, in feet, of BC is the square root of  √242 and, The length, in feet, of CF is the square root of √363

Cube:

In geometry, a cube is a three-dimensional solid object bounded by six faces, facets, or square sides, with three points of intersection at each vertex. Seen from a certain angle, it is a hexagon and its canvas is often represented by a cross.

Cube is the only regular hexahedron and one of the five Platonic solids. It has 6 faces, 12 edges and 8 vertices. Cube is also a cube, an equilateral cuboid, a rhombus and a 3-sonohedron.

Three orientations are square prisms and four orientations are triangular trapezoids. A cube is twice as large as an octahedron. It has cubic or octahedral symmetry. Cube is the only convex polyhedron whose faces are square.

Then the length CB is given by the Pythagorean theorem as:

CB = √(AC² +AB²)

     = √{(2 cm)² + (√2 cm)²}

     = √(4 +2) cm

CB = √6 cm

Now,

The length, in feet, of BC is the square root of  

√242

And,

The length, in feet, of CF is the square root of  

√363

Complete Question:

A cube. The top face has points C, A, B, D and the bottom face has points G, E, F, H. Diagonals are drawn from B to C and from C to F. Side B F is 11 feet.

What are the exact lengths of BC and CF?

The length, in feet, of BC is the square root of

The length, in feet, of CF is the square root of

Learn more about Square Root:

https://brainly.com/question/13953405

#SPJ4

Answer:

The length, in feet, of BC is the square root of

✔ 242

The length, in feet, of CF is the square root of

✔ 363

Step-by-step explanation:

The probability that exactly 10 out of 23 cars will not have engine failure is 0.007638.

Step-by-step explanation: First, calculate the probability of an engine failing in five years with no routine maintenance, which is 27.5%. This can be written as a decimal, 0.275.Next, calculate the probability of an engine not failing in five years with routine maintenance. This probability is 100%-27.5% = 72.5%, written as a decimal 0.725.

Now, using the Binomial Distribution formula (nCr), calculate the probability of exactly 10 engines not failing out of 23 cars, where n = 23, r = 10 and p = 0.725. The equation would be [tex](23C10)*(0.725^{10})*(0.275^{13}) = 0.0076379904[/tex]

Finally, round the result to 6 decimal places, giving an answer of 0.007638.

See more about probability at: https://brainly.com/question/13604758

#SPJ11

Answer:

How to solve a ratio problem:

Add together the parts of the ratio to find the total number of shares.

Divide the total amount by the total number of shares.

Multiply by the number of shares required.

pls mark me brainliest

A unity feedback control system is characterized by an open-loop transfer function G(s)H(s)=k/s(s+10). The system gain k so that the system will have a damping ratio of 0.5 is 4. The corresponding rise time is 2.3s, settling time is 4.4s, and peak overshoot is 0.26.

To determine the system gain k so that the system will have a damping ratio of 0.5, we can use the equation  ζ=1/2ωn. Rearranging the equation yields k=2ωn2. Using the damping ratio of 0.5, this yields k=4.
For this value of k, the rise time, settling time, and peak overshoot can be determined using the following equations:
Rise Time: Tr=4.6/ωn
Settling Time: Ts=4.4/ζωn
Peak Overshoot: Mp=e^(-ζπ/√1-ζ^2)
Given that the damping ratio is 0.5 and the system is subjected to a step input of 1V, we can determine the rise time, settling time, and peak overshoot.
Rise Time: Tr=4.6/ωn=4.6/2=2.3s
Settling Time: Ts=4.4/0.5ωn=4.4/1=4.4s
Peak Overshoot: Mp=e^(-0.5π/√1-0.5^2)=0.26

For more questions on feedback control system

https://brainly.com/question/17516264
#SPJ11

The slope in the equation b = 0.29h + 1.35 is the measure of the rate at which the bike frame size changes with the height of the rider.

The slope in the equation b = 0.29h + 1.35 refers to the coefficient of the variable h, which represents the height of the rider. The slope is the measure of the rate at which the bike frame size changes with the height of the rider.

In this equation, the slope is 0.29, which means that for every inch increase in the rider's height, the bike frame size increases by 0.29 inches. The slope is a crucial component of the equation as it determines the proportionality of the two variables.

Moreover, the slope is essential in analyzing the relationship between the rider's height and the bike frame size.

It plays a vital role in determining the appropriate size of the BMX bike frame and analyzing the relationship between the two variables.

To know more about equation here

https://brainly.com/question/10413253

#SPJ4

Complete Question:

Purchasing the correctly sized BMX bike is based on the height of the rider. In order to fit a customer, the salesman can use the equation b 0.29h +1.35 where b is the size of the BMX bike frame in inches and h is the height of the rider in inches.

Which sentence explains the slope in the equation?

The better understanding of the data, making it easier to draw conclusions and make decisions based on the data.

In statistics, the spread of the data is used to describe the variability or deviation of a set of data. The location of the data is used to determine the center of the data, and the shape of the data describes the distribution of the data. When it comes to the variable number of care types sp unable to get (acv nocarsum), the data should be analyzed using the appropriate graph(s) and descriptive statistics to determine its shape, location, and spread.
Descriptive statistics:
In descriptive statistics, measures such as mean, mode, median, standard deviation, variance, and range are used to analyze data. These statistics provide a summary of the data in the form of numerical values, making it easy to identify patterns, outliers, and other characteristics of the data.
Graphs:
Graphs are also used in statistical analysis to visually represent the data. There are different types of graphs that can be used, depending on the type of data being analyzed. Commonly used graphs in statistical analysis include histograms, scatterplots, boxplots, and line graphs.
To describe the shape, location, and spread of the data for the number of care types sp unable to get (acv nocarsum) variable, the following steps should be followed:

Step 1: Collect the data.
The first step is to collect the data on the number of care types sp unable to get (acv nocarsum) variable. This data can be obtained from various sources such as surveys, questionnaires, or observational studies.

Step 2: Determine the center of the data.
The center of the data can be determined using measures such as mean, mode, or median. The mean is the average of the data, while the median is the middle value of the data when arranged in order of magnitude. The mode is the value that appears most frequently in the data.

Step 3: Determine the variability of the data.
The variability of the data can be determined using measures such as variance or standard deviation. The variance is the average of the squared differences between each data point and the mean, while the standard deviation is the square root of the variance.

Step 4: Determine the shape of the data.
The shape of the data can be determined using graphs such as histograms, boxplots, or line graphs. Histograms show the distribution of the data, while boxplots show the quartiles and outliers of the data.

Step 5: Interpret the results.
Once the data has been analyzed using the appropriate graph(s) and descriptive statistics, the results should be interpreted to describe the shape, location, and spread of the data for the number of care types sp unable to get (acv nocarsum) variable. This will provide a better understanding of the data, making it easier to draw conclusions and make decisions based on the data.

Learn more about Conclusions

brainly.com/question/18119893

#SPJ11

Answer:

6.9 or 7.0 .

Step-by-step explanation:

*Note that ^2 means raised to the power of two or squared

a^2 + b^2 = c^2

The hypotenuse is always the C, and the leg can be either a or b.

Fill in the blanks with the numbers that we have:

Hypotenuse: 7.7 | Leg: 3.4

3.4^2 + b^2 = 7.7^2

Square the numbers given

3.4 x 3.4 = 11.56

7.7 x 7.7 = 59.29, which leads us to:

11.56 + b^2 = 59.29

To find what b equals, we need to subtract 11.56 from 59.29

59.29 - 11.56 = 47.73

b^2 = 47.73

We need to take the square root of 47.73 to find b. b and b^2 are two different things.

The square root of 47.73 is about 6.90869017977. It asks for the answer to be rounded to the nearest tenth, giving us 6.9 or 7.0.

If the hypothesis test is performed to determine if the proportion of all six packs of seltzers sold in a particular grocery store near a college campus that are alcoholic exceeds 50% Then complement of the P-value gives the probability that the null hypothesis is true, which is 1 minus 0.0047, or 0.9953.

The probability the null hypothesis is true is 1-0.0047 = 0.9953 because ,

The given P-value is 0.0047,

which is the probability of observing a test statistic as extreme as 2.60 or more extreme if the null hypothesis is true. Since this P-value is less than the significance level of 0.05 (assuming a typical significance level), we reject the null hypothesis and conclude that the proportion of all six packs of seltzers sold in the grocery store that are alcoholic exceeds 50%.

Therefore, statement (a) is true and all the other statements are incorrect. The complement of the P-value gives the probability that the null hypothesis is true, which is 1 minus 0.0047, or 0.9953.

To learn more about the 'null hypothesis':

https://brainly.com/question/4436370

#SPJ11

To solve this inequality, we must first isolate the absolute value on one side of the equation.

Step 1: Add 5 to both sides of the equation.

−2x−5 + 5 ≤ 5 + 5

Step 2: Simplify the left side.

−2x ≤ 10

Step 3: Divide both sides by -2.

x ≥ -5

Step 4: Graph the solution on a number line.

The solution set is {x | x ≥ -5}

The most distance Talia can go each day while staying within her budget is 320 miles.

In this case, our goal is to write an inequality before moving on to solve it.

We begin with the daily rental fee and the cost per mile.

This is stated as $30 per day and $0.20 per mile in the question.

She is required to spend a total of $94.

This means that the total cost of the rental automobile and the cost per mile must be $94 or less.

Let m be the maximum number of miles she can travel.

Hence, we may write the inequality as follows: 30 + 0.2 m 94.

This inequality is what we can now solve;

0.2m ≤ 94 - 30

0.2m ≤ 64

m ≤ 64/0.2

320 miles = m

The most distance Talia can go each day while staying within her budget is 320 miles.

To know more about inequality, click the below link

https://brainly.com/question/30231190

#SPJ4

Answer:

  r ≈ 44.25 cm

Step-by-step explanation:

You want the hypotenuse of a right triangle in which the side adjacent to the angle of 57° is 24.1 cm.

The cosine relation is ...

  Cos = Adjacent/Hypotenuse

  cos(57°) = (24.1 cm)/r

Solving for r gives ...

  r = (24.1 cm)/cos(57°) ≈ 44.25 cm

The length r is about 44.25 cm.

__

Additional comment

The calculator shown in the attachment has its angle mode set to degrees.

<95141404393>

The interest charge per month would be around $[tex]532.02[/tex], and the principal payment per month would be about $[tex]399.09[/tex].

Your hobbies are the things you find enjoyable to do and the things that you prefer to learn more about. A lack of intriguing conversation: Interesting things hold your attention and arouse your curiosity.

The cost of borrowing money is called interest, and it is typically stated as a percent, such as an annualized rate (APR). By utilizing the money, debtors may accrue interest to lenders, or lenders may pay the interest to borrowers.

We will use annuity formula, which is: [tex]P=C(\frac{1-(1+r)^{-n} }{r} )[/tex]

[tex]P[/tex] is [tex]105,000[/tex]

[tex]C[/tex] is what we need

[tex]r[/tex] is the [tex]0.045/12 = 0.00375[/tex]

[tex]n[/tex] is [tex]12*30 = 360[/tex]

[tex]P=C[\frac{1-(1+r)^{-n} }{r} ][/tex]

[tex]105,000=C[\frac{1-(1+0.00375)^{-360} }{0.00375} ][/tex]

[tex]1.5,000=C[197.3612][/tex]

[tex]C=532.02[/tex]

So monthly payment would be around [tex]532.02[/tex]

Now,

With each point purchase, the interest rate goes down by [tex]0.25[/tex]%, so for [tex]2[/tex] points it will be [tex]4.5[/tex]%[tex]- 2(0.25) = 4[/tex]%

Also, since [tex]20[/tex]% down payment, the loan amount would be [tex](0.8)(105,000) = 84,000[/tex].

Putting these values into the annuity formula we have:

[tex]84000=C[\frac{1-(1+.0..33)^{-360} }{0.0033} ][/tex]

[tex]84000=C(210.47)[/tex]

[tex]C=399.09[/tex]

The monthly payment would be around $[tex]399.09[/tex]

To know more about interest visit:

https://brainly.com/question/13421160

#SPJ1

The new coordinates of the two points after rotating the parallel lines 180 degrees clockwise are (2, -7) and (-8, 5).

What are parallel lines?

In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet.

If the set of parallel lines contains the points (-2, 7) and (8, -5), then the two lines are parallel to each other and have the same slope. We can find the slope of the line that passes through these two points using the slope formula:

slope = (y2 - y1) / (x2 - x1)

slope = (-5 - 7) / (8 - (-2))

slope = -12 / 10

slope = -6 / 5

So, the equations of the two parallel lines are:

y - 7 = (-6 / 5)(x + 2) --- equation 1

y + 5 = (-6 / 5)(x - 8) --- equation 2

To rotate the lines 180 degrees clockwise, we need to negate both the x and y coordinates of the points on the lines. That is, we need to replace each point (x, y) with the point (-x, -y).

So, after the rotation, the new coordinates of the two points will be:

(-(-2), -7) = (2, -7) --- for point (-2, 7)

(-(8), -(-5)) = (-8, 5) --- for point (8, -5)

Learn more about parallel lines on:

https://brainly.com/question/30097515

#SPJ1