Fill in the following blanks to prove that n 2^1 n < 2^n n+1 < 2^(n+1) is Box 3 Options: True | False Next, assume that Box 4 Options: 1 < 2^1 k + 1 < 2^(k+1) k < 2^k as we attempt to prove Box 5 Options: k < 2^k k + 1 < 2^(k+1) 2 < 2^1 Therefore, we can conclude that Box 6 Options: k < 2^k k + 1 < 2^(k+1) 2^1 < 2^k k + 2 < 2^(k+2)

Answer:

D

Step-by-step explanation:

I don't know how to eliminate the wrong answers.

Two line segments which have one end at a diameter and the other end meeting at a common point, make a 90 degree angle.

A is made that way, so A is 90 degrees.

Answer:

Step-by-step explanation:

I believe it is 90

Answer:

$935.76

Step-by-step explanation:

BOND VALUATION Asiana Fashion's bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 8% and thebyield to maturity is 9%.What is the bond's current market price?​

Step 1

We find the Present value factor of sum

The formula =

(1 + i)^n

Where

i = maturity rate = 9% = 0.09

n = number of years = 10 years

Present Value = ( 1 + 0.09)^-10

= 0.4224

Step 2

We find the present value factor of annuity

The formula is given as:

1 - (1+i)^-n / i

i = maturity rate = 9% = 0.09

n = number of years = 10 years

= 1 - (1 + 0.09)^-10 /0.09

= 1 - 0.4224 /0.09

= 0.5775 /0.09

= 6.417

Step 3

The bond's current market price is calculated as:

= PV factor of Sum × Par Value + PV factor of annuity × coupon payment

Coupon payment is calculated as:

= Coupon interest × par value

= 8% × 1000

= 80

Hence,

= 0.4224 × 1,000 + 6.417 × 80

= 422.4 + 513.36

= 935.76

In this exercise we have to use the knowledge of finance to calculate the corrective value of the market place, in this way we find that:

[tex]\$935.76[/tex]

We find the Present value factor of sum, by the formula of:

[tex](1 + i)^n[/tex]

Where:

Substituting the values ​​in the formula as;

[tex]Present \ Value = ( 1 + 0.09)^{-10} = 0.4224[/tex]

We find the present value factor of annuity, by the formula as:

[tex]1 - (1+i)^{-n} / i[/tex]

Where:

Substituting the values ​​in the formula as;

[tex]= 1 - (1 + 0.09)^{-10} /0.09\\= 1 - 0.4224 /0.09\\= 0.5775 /0.09\\= 6.417[/tex]

The bond's current market price is calculated as:

[tex]= PV \ factor\ of\ Sum * Par\ Value + PV\ factor\ of\ annuity * coupon\ payment[/tex]

Coupon payment is calculated as:

[tex]= Coupon\ interest * par\ value\\= 8\% * 1000= 80[/tex]

So continue the calcule;

[tex]= 0.4224 *1,000 + 6.417 * 80\\= 422.4 + 513.36\\= 935.76[/tex]

See more about market place at brainly.com/question/24518027

Answer:

8.8 pounds

Step-by-step explanation:

Given the following :

Combined weight loss which occurred within a week = 28 kg

Number of days in a week = 7 days

1 kilogram (kg) = 2.2 pounds

Combined weight loss in pounds that occurs within a week:

Weight loss in kg × 2.2

28kg * 2.2 = 61.6 pounds

Assume weight loss occurred at a constant rate :

Weight lost by the group per day :

(Total weight loss / number of days in a week)

(61.6 pounds / 7)

= 8.8 pounds daily

Answer:

88

Step-by-step explanation:

Found the answer and I am doing the quiz rn lel

Answer:

8

Step-by-step explanation:

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

8x→1

7y→1

The largest exponent is the degree of the polynomial.

1

The leading term in a polynomial is the term with the highest degree.

8x

The leading coefficient of a polynomial is the coefficient of the leading term.

____________________________________________________________

The leading term in a polynomial is the term with the highest degree.

8x

The leading coefficient in a polynomial is the coefficient of the leading term.

8

List the results.

Polynomial Degree: 1

Leading Term: 8x

Leading Coefficient: 8

Hope This Helps!!!

Answer:

a) f(6)=(6)^2+4(6)+1=65

b)f (x+9)=(x+9)^2+4 (x+9)+1=(x^2+18x+81)+(4x+36)+1=x^2+22x+117

f (-x)=(-x)^2-4x+1

Answer:

The population that gives the maximum sustainable yield is 45000 swordfishes.

The maximum sustainable yield is 202500 swordfishes.

Step-by-step explanation:

Let be [tex]f(p) = -0.01\cdot p^{2}+9\cdot p[/tex], the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)

First Derivative Test

[tex]f'(p) = -0.02\cdot p +9[/tex]

Let equalize the resulting expression to zero and solve afterwards:

[tex]-0.02\cdot p + 9 = 0[/tex]

[tex]p = 450[/tex]

Second Derivative Test

[tex]f''(p) = -0.02[/tex]

This means that result on previous part leads to an absolute maximum.

The population that gives the maximum sustainable yield is 45000 swordfishes.

The maximum sustainable yield is:

[tex]f(450) = -0.01\cdot (450)^{2}+9\cdot (450)[/tex]

[tex]f(450) =2025[/tex]

The maximum sustainable yield is 202500 swordfishes.

Answer:

[tex]\large \boxed{31/63}[/tex]

Step-by-step explanation:

5/7 - 2/9

Make denominators equal by LCM.

(5 × 9)/(7 × 9) - (2 × 7)/(9 × 7)

45/63 - 14/63

Subtract fractions since denominators are equal.

(45 - 14)/63

31/63

Answer:

[tex]\frac{31}{63}[/tex]

Step-by-step explanation:

Therefore, the answer is [tex]\frac{31}{63}[/tex].

Answer:c

Step-by-step explanation:

Answer: The answer is C.

Hope this helps you!

Answer:

(a) The probability that X is at most 30 is 0.9726.

(b) The probability that X is less than 30 is 0.9554.

(c) The probability that X is between 15 and 25 (inclusive) is 0.7406.

Step-by-step explanation:

We are given that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked. A random sample of 200 shafts is taken.

Let X = the number among these that are nonconforming and can be reworked

The above situation can be represented through binomial distribution such that X ~ Binom(n = 200, p = 0.11).

Here the probability of success is 11% that this much % of all steel shafts produced by a certain process are nonconforming but can be reworked.

Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).

So, the new mean of X, [tex]\mu[/tex] = [tex]n \times p[/tex] = [tex]200 \times 0.11[/tex] = 22

and the new standard deviation of X, [tex]\sigma[/tex] = [tex]\sqrt{n \times p \times (1-p)}[/tex]

                                                                  = [tex]\sqrt{200 \times 0.11 \times (1-0.11)}[/tex]

                                                                  = 4.42

So, X ~ Normal([tex]\mu =22, \sigma^{2} = 4.42^{2}[/tex])

(a) The probability that X is at most 30 is given by = P(X < 30.5)  {using continuity correction}

        P(X < 30.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{30.5-22}{4.42}[/tex] ) = P(Z < 1.92) = 0.9726

The above probability is calculated by looking at the value of x = 1.92 in the z table which has an area of 0.9726.

(b) The probability that X is less than 30 is given by = P(X [tex]\leq[/tex] 29.5)    {using continuity correction}

        P(X [tex]\leq[/tex] 29.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{29.5-22}{4.42}[/tex] ) = P(Z [tex]\leq[/tex] 1.70) = 0.9554

The above probability is calculated by looking at the value of x = 1.70 in the z table which has an area of 0.9554.

(c) The probability that X is between 15 and 25 (inclusive) is given by = P(15 [tex]\leq[/tex] X [tex]\leq[/tex] 25) = P(X < 25.5) - P(X [tex]\leq[/tex] 14.5)   {using continuity correction}

       P(X < 25.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{25.5-22}{4.42}[/tex] ) = P(Z < 0.79) = 0.7852

       P(X [tex]\leq[/tex] 14.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{14.5-22}{4.42}[/tex] ) = P(Z [tex]\leq[/tex] -1.70) = 1 - P(Z < 1.70)

                                                          = 1 - 0.9554 = 0.0446

The above probability is calculated by looking at the value of x = 0.79 and x = 1.70 in the z table which has an area of 0.7852 and 0.9554.

Therefore, P(15 [tex]\leq[/tex] X [tex]\leq[/tex] 25) = 0.7852 - 0.0446 = 0.7406.

Answer:

92 inches squared

Step-by-step explanation:

T/P = 8 * 3

L/R = 3 * 2

F/B = 8 * 2

Solving for surface area!

2(24) + 2(6) + 2(16) = 92

Answer:

Option A (repeated measures design) is the correct option.

Step-by-step explanation:

The other three options are not related to the given instance. So that alternative A would be the correct choice.

Answer:

The first pyramid:

      63x

  39x  24x  

23x  16x  8x

The second pyramid:

     162x

 82x  80x  

4x  78x  2x

The third pyramid:

     12a+2b

9a+b   3a+b  

9a     b     3a

The fourth pyramid:

      -19a

  -5a   -14a  

3a   -8a  -6a

Step-by-step explanation:

All that an alegbra pyramid is is adding the two terms below it.

So you can see how I added the terms that lied below each number, such as in number 1:  I added 23x and 16x to get me 39x, and I added 16x and 8x to get me 24.

Hope this helped!

Answer:

The percentage is [tex]P(350 < X 650 ) = 86.6\%[/tex]

Step-by-step explanation:

From the question we are told that

   The population mean is  [tex]\mu = 500[/tex]

     The standard deviation is  [tex]\sigma = 100[/tex]

The  percent of people who write this exam obtain scores between 350 and 650    

    [tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <\frac{ X - \mu }{ \sigma } < \frac{650 - 500}{ 100} )[/tex]

Generally  

               [tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]

   [tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <Z < \frac{650 - 500}{ 100} )[/tex]

   [tex]P(350 < X 650 ) = P(-1.5<Z < 1.5 )[/tex]

   [tex]P(350 < X 650 ) = P(Z < 1.5) - P(Z < -1.5)[/tex]

From the z-table  [tex]P(Z < -1.5 ) = 0.066807[/tex]

   and [tex]P(Z < 1.5 ) = 0.93319[/tex]

=>    [tex]P(350 < X 650 ) = 0.93319 - 0.066807[/tex]

=>  [tex]P(350 < X 650 ) = 0.866[/tex]

Therefore the percentage is  [tex]P(350 < X 650 ) = 86.6\%[/tex]

Answer:

Step-by-step explanation:

Since m and k are the parallel lines and a transverse 'l' is intersecting these lines at two different points.

- Opposite angles at the point of intersection of parallel lines and the transverse will be the vertical angles.

∠1 ≅ ∠3, ∠2 ≅ ∠4, ∠5 ≅ ∠8 and ∠6 ≅ ∠7 [Vertical angles]

- Pair of angles between parallel lines 'k' and 'm' but on the opposite side of the transversal are the alternate interior angles.

∠4 ≅ ∠6 and ∠3 ≅ ∠5 [Alternate interior angles]

- Angles having the same relative positions at the point of intersection are the corresponding angles.

∠2 ≅ ∠6, ∠3 ≅ ∠8, ∠4 ≅ ∠7 and ∠1 ≅ ∠5 [Corresponding angles]

- Co interior angles are the angles between the parallel lines located on the same side of the transversal.

∠4 and ∠5, ∠3 and ∠6 [Co interior angles]

- Co exterior angles are the angles on the same side of the transverse but outside the parallel lines.

∠2 and ∠8, ∠1 and ∠7 [Co exterior angles]

Answer:

the probability will be 0.

Step-by-step explanation:

0.12%= 0.0012= 3/2500.

Answer:

The answer is "253"

Step-by-step explanation:

In the given- equation there is mistype error so, the correct equation and its solution can be defined as follows:

Given:

[tex]\bold{\frac{dn}{dt} = 6\sqrt{t+1}}\\[/tex]

[tex]\to dn= 6\sqrt{t+1} \ \ dt.....(a)\\\\[/tex]

integrate the above value:

[tex]\to \int dn= \int 6\sqrt{t+1} \ \ dt \\\\\to n= \frac{(6\sqrt{t+1} )^{\frac{3}{2}}}{\frac{3}{2}}+c\\\\\to n= \frac{(12\sqrt{t+1} )^{\frac{3}{2}}}{3}+c\\\\[/tex]

When the value of n=1 then t=0

[tex]\to 1= \frac{12(0+1)^{\frac{3}{2}}}{3}+c\\\\ \to 1= \frac{12(1)^{\frac{3}{2}}}{3}+c\\\\\to 1-\frac{12}{3}=c\\\\\to \frac{3-12}{3}=c\\\\\to \frac{-9}{3}=c\\\\\to c=-3\\[/tex]

so the value of  n is:

[tex]\to n= \frac{(12\sqrt{t+1} )^{\frac{3}{2}}}{3}-3\\\\[/tex]

when we put the value t= 15 then,

[tex]\to n= \frac{(12\sqrt{15+1} )^{\frac{3}{2}}}{3}-3\\\\\to n= \frac{(12\sqrt{16} )^{\frac{3}{2}}}{3}-3\\\\\to n= \frac{(12\times 64)}{3}-3\\\\\to n= (4\times 64)-3\\\\\to n= 256-3\\\\\to n= 253[/tex]

Answer:

Its 10x^2+12

Step-by-step explanation:

Answer:

-10X^2+12

Step-by-step explanation:

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

   Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

[tex]\frac{(17)(3.141593)}{12}[/tex]

= [tex]\frac{53.407075}{12}[/tex]

= [tex]4.45059[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

If this helped you, could you maybe give brainliest..?

Also Have a great day/night!

❀*May*❀

I have an answer and explanation but I can't type so search up the question you asked and you should get an answer and explanation from s0cratic.

Answer:

6 years

Step-by-step explanation:

A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now. This is an exponential function, An exponential function is given by:

[tex]y=ab^x[/tex]

Let x be the number of years and y be the allowance. The initial allowance is $8, this means at x = 0, y = 8

[tex]y=ab^x\\8=ab^0\\a=8[/tex]

Since it increases by 20% each year, i.e 100% + 20% = 1 + 0.2 = 1.2. This means that b = 1.2

Therefore:

[tex]y=ab^x\\y=8(1.2^x) \\[/tex]

To find the number of years will it take to reach $20 per month, we substitute y = 20 and find x

[tex]20=8(1.2)^x\\20/8=1.2^x\\1.2^x=2.5\\Taking \ natural\ log\ of \ both\ sides:\\ln(1.2^x)=ln2.5\\xln(1.2)=0.9163\\x=0.9163/ln(1.2)\\x=5.026[/tex]

x = 6 years to the nearest year

Answer:

5 years

Step-by-step explanation:444

13226/29= 456.068965517

Answer:

The velocity is  [tex]v = 886.96 \ m/s[/tex]

Step-by-step explanation:

From the question we are told that

    The period of each revolution is  [tex]T = 1\ day = 24 \ hours[/tex]

    The angle  is [tex]\theta = 30^o[/tex]

     The radius is  [tex]r = 3387.5 \ miles[/tex]

Generally the linear speed is  mathematically represented as

        [tex]v = w * r[/tex]

Where  [tex]w[/tex] is the angular speed which is mathematically represented as

       [tex]w = \frac{2 \pi }{T}[/tex]

substituting values

       [tex]w = \frac{2 *3.142 }{24}[/tex]

        [tex]w = 0.2618 \ rad/s[/tex]

Thus  

         [tex]v = 0.261833 * 3387.5[/tex]

        [tex]v = 886.96 \ m/s[/tex]

Answer:

$5

Step-by-step explanation:

Let the notebook cost x, then Mark spent:

Notebook costs $5

Answer:

C. 50 degrees

Step-by-step explanation:

Because 6x + 5x = 110° and x = 10

5×10 = FEG 50°

Answer:

Step-by-step explanation:

∠a is alternate interior angle to ∠ECD

∠b is alternate interior angle to ∠BCD

so:

If AB || CD then:

m∠a = m∠ECD = 25° + 42° = 67°

m∠b = 42°

Answer:

We conclude that the population mean is equal to 490.

Step-by-step explanation:

We are given that a random sample of 15 observations is selected from a normal population. The sample mean was 495 and the sample standard deviation 9.

Let [tex]\mu[/tex] = population mean.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 490      {means that the population mean is equal to 490}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 490     {means that the population mean is different from 490}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                               T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_1_4[/tex]

where, [tex]\bar X[/tex] = sample mean = 495

            s = sample standard deviation = 9

             n = sample of observations = 15

So, the test statistics =   [tex]\frac{495-490}{\frac{9}{\sqrt{15} } }[/tex]  ~ [tex]t_1_4[/tex]

                                     =  2.152

The value of t-test statistics is 2.152.

Now, at a 0.01 level of significance, the t table gives a critical value of -2.977 and 2.977 at 14 degrees of freedom for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.

Therefore, we conclude that the population mean is equal to 490.

Answer:

23 miles per gallon

Step-by-step explanation:

414 miles = 18 gallons

=> 18/18 gallons = 414/18 miles

=> 1 gallon = 23 miles

So, she drove 23 miles per gallon.

Question Completion:

WACC = 10.0%

Opportunity cost = $100,000

Net equipment cost (depreciable basis) = $65,000

Straight-line deprec. rate for equipment = 33.333%  

Sales revenues, each year = $123,000

Operating costs (excl. deprec.), each year = $25,000

Tax rate = 35%

Answer:

Century Roofing

Project's NPV is: ($6,578)

Step-by-step explanation:

a) Data and Calculations:

WACC = 10.0%

Opportunity cost = $100,000

Net equipment cost (depreciable basis) = $65,000

Straight-line deprec. rate for equipment = 33.333%  

Sales revenues, each year = $123,000

Operating costs (excl. deprec.), each year = $25,000

Tax rate = 35%

Cash outflow in year 0 = $165,000 (Opportunity and new equipment costs)

Annual Cash inflow = $123,000 - $25,000 - $34,300 = $63,700

PV of annuity for 3 years at 10% = $158,422 ($63,700 x 2.487)

NPV = Cash inflow minus Cash outflow

= $158,422 - $165,000

= ($6,578)

Negative NPV

b) Since Century Roofing could have realized $100,000 from the sale of the building if it decides not to open the new warehouse, this opportunity cost is factored into the calculation of the Net Present Value.  It becomes a present cash outflow.  Century Roofing's opportunity cost is defined as the loss of $100,000 being the future return from the best alternative project when it chooses to build the new warehouse instead of selling off the building.

Answer:

The work done by the force is 42.4 Joules

Step-by-step explanation:

The force F = 7 pounds

angle to the horizontal that the force acts ∅ = 30°

The object is moved a distance d = 7 feet

The coordinate  (0 comma 0 )to (7 comma 0 ), indicates that the movement started from the origin, and is along the x-axis.

The work done by this force = F cos ∅ x d

==> 7 cos 30° x 7

==> 7 x 0.866 x 7 = 42.4 Joules

Answer:

Step-by-step explanation:

[tex](1+6i)-(7+3i) ?\\Group\:the\:real\:part\:and\:the\:imaginary\\\:part\:of\:the\:complex\:number\\\left(a+bi\right)\pm \left(c+di\right)=\left(a\:\pm \:c\right)+\left(b\:\pm \:d\right)i\\=\left(1-7\right)+\left(6-3\right)i\\1-7=-6\\6-3=3\\=-6+3i[/tex]