Proving explicit formulas for recurrence relations by induction. Prove each of the following statements using mathematical induction (b) Define the sequence {bn} as follows: • bo = 1 • bn = 2b_n-1 + 1 for n ≥ 1 Prove that for n ≥ 0, bn = 2^n+1 -1.

True. Statistical process control is commonly used in service industries, including blood testing labs, to monitor and analyze processes and determine normal levels of variation.

These normal levels of variation are often used as the basis for setting specifications and determining if a process is in control or out of control. Therefore, they can be considered the "voice of the specification" in service industries.

True. Statistical process control is used in service industries like a blood testing lab to determine normal levels of variation. Normal levels of variation are considered the voice of the specification. This helps to maintain quality and control the process.

Learn more about variation at: brainly.com/question/13977805

#SPJ11

Answer:

-5, -3, -1, 1

Step-by-step explanation:

Answer:

coordinates of the orthocenter = (8, 6)

Step-by-step explanation:

I have drawn a diagram showing this triangle with the vertices. I have also drawn altitude from B perpendicular to AC at point E.

I have also drawn altitude from from A perpendicular to BC at point D.

Now, we will find the slope of AC from the line slope equation; (y - y1) = m(x - x1)

m = (y - y1)/(x - x1)

Our coordinates are; A(5,3), B(8,6), C(0,14)

Thus;

Slope of AC; m = (14 - 3)/(0 - 5)

m = -11/5

Since BE is perpendicular to AC, slope of BE = -1/slope of AC = -1/(-11/5) = 5/11

Thus, equation of BE is;

(y - 6) = (5/11)(x - 8)

Multiply through by 11 to get;

11y - 66 = 5x - 40

11y - 5x = 66 - 40

11y - 5x = 26

Slope of BC is; m = (14 - 6)/(0 - 8) = 8/-6 = -1

AD is perpendicular to BC, thus slope of AD = -1/-1 = 1

Equation of AD is;

(y - 3) = 1(x - 5)

y - 3 = x - 5

y = x - 5 + 3

y = x - 2

Putting x - 2 for y in equation of BE, we have;

11(x - 2) - 5x = 26

11x - 22 - 5x = 26

6x - 22 = 26

6x = 26 + 22

6x = 48

x = 48/6

x = 8

Put 8 for x in equation AD, then y = 8 - 2 = 6

coordinates of the orthocenter = (8, 6)

Salut/Hello!

Answer: w = 20 cm and l = 28 cm

Step-by-step explanation:
l - length
w - width
P - perimeter
/ - fraction line
=> - results

we know that P = 2 x (l + w)
we also know that our ratio is l/w = 7/5

l/w = 7/5 => l = 7/5 x w
so now we can go back to the perimeter and replace l

96 = 2 x (7/5 x w + w)
96 = 2 x (7/5 x w/1 + w)   Why w/1? - We can't multiply unless w is also in a fraction, so we put it as w/1
96 = 2 x (7w/5 + w)
96 = 2 x (7w/5 + w/1)  and we amplify w/1 with 5
96 = 2 x (7w/5 + 5w/5)
96 = 2 x 12w/5
48 = 12w/5
48/1 = 12w/5
48 x 5 = 12w
240 = 12w
w = 20 cm

with that we can find l
96 = 2 x (l + 20)
48 = l + 20
l = 48 - 20
l = 28 cm

I hope it was helpful! :]

The absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex for this problem are given as follows:

(1, -2).

As the slope of the line is of 1, the leading coefficient is given as follows:

a = 1.

Hence the absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

More can be learned about absolute value functions at brainly.com/question/3381225

#SPJ1

Answer: 11 Kilometre

Step-by-step explanation:

The explanation has been provided in the attached file. Please find the attachment.

Answer: The answer is m^2

Step-by-step explanation:

Answer:

5.63

Step-by-step explanation:

The Slope Intercept Formula is written as y=mx + b

In this case, cost = y, m = 5/63, and b = 33.16

y = 5.63 + 33.16

Since rate of change is the same as slope, or m, the rate of change = 5.63

-Chetan K

Answer:

A

Step-by-step explanation:

37 is greater than 9

Answer:

16 apples

Step-by-step explanation:

If the original ratio is 4:7.

Then we multiply both numbers by 4. Since 7 x 4 is 28.

So now you have (4x4):(7x4)

Your final ratio is 16 apples : 28 oranges

What must have motivated the behavior of the Investor to commit to such a large stock is; Option C: High Total Earnings

A) Low real returns; This cannot be his motivation to buy large shares because real return is what is earned on an investment after accounting for taxes and inflation. Thus, the lower, the less encouraging to investors.

B) Higher shares costs; This only means that the share cost is currently high which indicates strength of the company but it does not guarantee that it will scale up at a very fast rate again.

C) High total earnings; Thus would be an encouragement to the investor because the higher the total earning potential of an investment, the more the profitability and the more attractive to others.

Read more about Stock Investments at; https://brainly.com/question/25818989

#SPJ1

Answer: 0, 50

Step-by-step explanation: (h=0), 0=2t+100

2t=100

t=50

hopefully this helps

Answer:

y = -1/5 + 7

Step-by-step explanation:

Substitute the point (1,2) for the x and the y in the equation, set the 4 to b since we are solving for b.

2 = -5(1) + b  now solve for b

2 = -5 + b

+5   +5

7 = b

we know that the slope must be the reciprocal for it to be perpendicular

y = -1/5 + 7 add b (7) to the equation and change the reciprocal

Answer:

205

Step-by-step explanation:

\(2000\times\left(\left(5+1)^2-1)\right.\right.\)

Evaluate the equation/expression:

205

I hope this helps you

:)

\(First,\:convert\:R\:as\:a\:percent\:to\:r\:as\:a\:decimal\\r = R/100\\r = 5/100\\r = 0.05\: rate\: per\: year\\\\Then\:solve\:the\:equation\:for\:A\\A = P(1 + r/n)nt\\A = 2,000.00(1 + 0.05/1)x^{1,2} \\A = 2,000.00(1 + 0.05)x^{2} \\A = $2,205.00\\A = $2,205.00\\\\A = P + I\:where\\P\: (principal) = $2,000.00\\I\: (interest) = $205.00\\\\Answer= $205.00\)

Answer:

x=34

Step-by-step explanation:

3x+1+2x+9=180

10+5x=180

5x=170

x=34

Answer:

Lets solve = 3/5 ÷ 1/2

3/5 ÷ 1/2

= 3/5 × 2/1

= 3 × 2/5 × 1

= 6/5

In mixed fraction its

\(1 \frac{1}{5} \)

____________________

Now lets solve "a" option

3/5 × 2

= 3 × 2/5 × 1

= 6/5

In mixed fraction

\(1 \frac{1}{5} \)

So option a = 3/5 x 2/1 is ur answer

is \( \sf \frac{3}{2} \times \frac{2}{1} [B]\)

\( \sf \frac{ 3}{5} \div \frac{1}{2} \)

\( \sf = \frac{3}{2} \times \frac{2}{1} [B]\)

Which multiplication expression is equal to 3/5 1/2 the answer is \( \sf \frac{3}{2} \times \frac{2}{1} [B]\).

Answer:

number = - 1

Step-by-step explanation:

let the number be n then twice the number is 2n , so

2n + 4 = n + 3 ( subtract n from both sides )

n + 4 = 3 ( subtract 4 from both sides )

n = - 1

The number is - 1

The total present value of these payments at the time the first payment is made is 1,735.85 (747.26 + 988.59).

To calculate the present value of these payments, we need to use the formula for the present value of an annuity:

\(PV = (P/i) x [1 - (1+i)^-n]\)

Where:
P = payment amount
i = annual effective rate
n = number of payments

Using this formula, we can calculate the present value of the first 10 payments:

\(PV = (100/0.07) x [1 - (1+0.07)^-10] = 747.26\)

To calculate the present value of the remaining 10 payments, we need to first calculate the payment amounts. To do

this, we can use the following formula:

\(Pn = P1 x (1 + g)^n\)

Where:
Pn = payment in year n
P1 = first payment amount
g = growth rate
n = number of years since first payment

For the 11th payment:

\(P11 = 105 x (1 + 0.05)^1 = 110.25\)

For the 12th payment:

\(P12 = 110.25 x (1 + 0.05)^1 = 115.76\)

And so on, until the 20th payment:

\(P20 = 163.32 x (1 - 0.05)^8 = 79.24\)

Now we can calculate the present value of these payments:

PV = \((110.25/0.07) x [1 - (1+0.07)^-10] + (115.76/0.07) x [1 - (1+0.07)^-9] + ... + (79.24/0.07) x [1 - (1+0.07)^-1]\)

PV = 988.59

for such more question on word problem

https://brainly.com/question/21405634

#SPJ11

you can reduce it to factors of degree 2 or less).

The two dice do not need to be identical. If it is possible, do it. If it is not possible, prove that it is not possible.

Some hints I got were to try to construct a pair of nonstandard dice such that the generating function for their sum matches the corresponding g.f. for a pair of standard dice and to note that the g.f. for a pair of standard dice can be factored quite a bit (you can reduce it to factors of degree 2 or less).

Learn more about Dice here:

https://brainly.com/question/2264527

#SPJ4

Answer:

Step-by-step explanation: π = 3.142

r = 10 cm

Area of the circle = 3.142 × 10²

Area = 3.142 × 100

Area = 314.2 cm²

The area of the required circle would be 149.590 cm² which is a radius of 6.9 cm.

The area of the circle is equal to the product of the square of the radius of the circle and pi.

A = πr²

where 'r' is the radius of the circle

We have been given that the radius of a circle is 6.9 cm.

So here r = 6.9 cm

the area of a circle = πr²

the area of a circle = π(6.9)²     [take π = 3.142]

the area of a circle = (3.142)(47.61)

the area of a circle = 149.590 cm²

Hence, the area of the required circle would be 149.590 cm².

Learn more about the area of the circle here:

brainly.com/question/19794723

#SPJ2

Answer:

73 ,,,,,,,,,,,,,,,,,,,,,,,

The symmetrical interval that includes 93% of the sample means is (3.2455 gallons per month, 3.5545 gallons per month) assuming the population follows a normal distribution.

To calculate the probabilities and identify the symmetrical interval, we'll use the provided information:

Given:

Population mean (μ) = 3.4 gallons per month

Population standard deviation (σ) = 0.85 gallons per month

Sample size (n) = 100

a. Probability that the sample mean will be less than 3.3 gallons per month: To calculate this probability, we need to use the sampling distribution of the sample mean, assuming the population follows a normal distribution. Since the sample size (n) is large (n > 30), we can approximate the sampling distribution as a normal distribution using the Central Limit Theorem. The mean of the sampling distribution is equal to the population mean (μ), which is 3.4 gallons per month. The standard deviation of the sampling distribution, also known as the standard error (SE), can be calculated as σ / √n:

SE = σ / √n

= 0.85 / √100

= 0.085 gallons per month

Now, we can calculate the z-score using the formula:

z = (x - μ) / SE

Substituting the values:

z = (3.3 - 3.4) / 0.085

= -0.1 / 0.085

= -1.1765

Using a standard normal distribution table or calculator, we can find the probability corresponding to a z-score of -1.1765. The probability that the sample mean will be less than 3.3 gallons per month is approximately 0.1190. Therefore, the probability is 0.1190.

b. Probability that the sample mean will be more than 3.6 gallons per month:

Similarly, we can calculate the z-score for this case:

z = (x - μ) / SE

= (3.6 - 3.4) / 0.085

= 0.2 / 0.085

= 2.3529

Using a standard normal distribution table or calculator, we find the probability corresponding to a z-score of 2.3529. The probability that the sample mean will be more than 3.6 gallons per month is approximately 0.0096.

Therefore, the probability is 0.0096.

c. Identifying the symmetrical interval that includes 93% of the sample means:

To find the symmetrical interval, we need to determine the z-scores corresponding to the tails of 93% of the sample means.

Since the distribution is symmetrical, we can divide the remaining probability (100% - 93% = 7%) equally between the two tails.

Using a standard normal distribution table or calculator, we find the z-score corresponding to a tail probability of 0.035 on each side. The z-score is approximately 1.8125.

The symmetrical interval is then given by:

=μ ± z * SE

=3.4 ± 1.8125 * 0.085

=(3.4 - 1.8125 * 0.085, 3.4 + 1.8125 * 0.085)

=(3.4 - 0.1545, 3.4 + 0.1545)

=(3.2455, 3.5545)

To know more about symmetrical interval,

https://brainly.com/question/32624935

#SPJ11

Answer:

a. +3

b. -12a

Step-by-step explanation:

Here, we want to know the steps that are involved in those unoccupied segments

let’s start with the output

6a + 18

So what turned a to 6a + 18

Let’s call that output x

Let’s reverse the last step that multiplied that term and a

Thus (6a + 18)/6 = a + 3

Thus the x-term we are looking for is + 3 before the multiplication by 6

Now for the second part;

a * 4 -3 = -12a

Step-by-step explanation:

Simplify the equation using algebra in order to find the value of g.

Multiply each side of the equation by 8 to remove the fraction from g:

\(8( \frac{g}{8} ) = 8( \frac{9}{12} )\)

\(g = 6\)

The town will have a population of 20683 after 5 years

Let the initial population be P₀

P₀ = 17000

Growth rate, R = 4% = 4/100 = 0.04

Time, T = 5

The population after 5 years will be given by the formula:

The town will have a population of 20683 after 5 years

The building's depression angle relative to the plane is found as  24.49°.

According to an aerial photographer who specializes in taking pictures of real estate properties.

The ideal shot should be taken at a height of around 406 feet and a distance of 891 feet from the structure.

Height h = 406 ft

Distance d =891 ft

The building's depression angle relative to the plane:

tan Ф = Height / Distance

tan Ф = 406 / 891

tan Ф = 0.455

Ф = 24.49°

Thus, the building's depression angle relative to the plane is found as  24.49°.

Know more about the angle of depression

https://brainly.com/question/15580615

#SPJ1

The products obtained from the reactions of (E)- and (Z)-hex-3-ene with D2 in the presence of a platinum catalyst are related as enantiomers.

Hence, the correct option is E.

Enantiomers are stereoisomers that are non-superimposable mirror images of each other. In this case, the (E)- and (Z)-isomers have different spatial arrangements around the C=C double bond. When they react with D2 in the presence of a platinum catalyst, the deuterium atoms add to the double bond, resulting in two new chiral centers.

Since the two isomers have different spatial arrangements around the double bond, the addition of deuterium atoms will produce enantiomeric products. Therefore, the products obtained from the reactions of (E)- and (Z)-hex-3-ene with D2 are related as enantiomers.

Hence, the correct option is E.

To know more about enantiomers here

https://brainly.com/question/29095975

#SPJ4

Answer:

$32.13

Step-by-step explanation:

IXL

The total cost will be;

⇒ $32.05

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Elijah bought a chest of drawers originally priced at $50.40 but on sale for 40% off.

Now,

Since, Elijah bought a chest of drawers originally priced at $50.40 but on sale for 40% off.

Hence, The sale price = 40% of $50.60

                                  = 40/100 × $50.60

                                  = $20.24

Thus, The price chest of drawers become = $50.40 - $20.24

                                                                 = $30.16

Since, The sales tax = 6.25%

Hence, The sales price = 6.25% of $30.16

                                    = 6.25/100 x 30.16

                                    = $1.89

Thus, The total cost = $30.16 + $1.89

                              = $32.05

Therefore, The total cost will be;

⇒ $32.05

Learn more about the percent visit:

https://brainly.com/question/24877689

#SPJ6

Answer:

y=7

Step-by-step explanation:

you would divide each term by 8 to get y=7 (8/8 and 66/8) :) hope this helps!!