Adam must fly home to city A from a business meeting in city B. One flight option flies directly to city A from​ B, a distance of about 456.2456.2 miles. A second flight option flies first to city C and then connects to A. The bearing from B to C is N2929degrees°​E, and the bearing from B to A is N59.759.7degrees°E. The bearing from A to B is S59.759.7degrees°​W, and the bearing from A to C is N78.978.9degrees°W. How many more frequent flyer miles will Adam receive if he takes the connecting flight rather than the direct​ flight? Adam would receive nothing more frequent flyer miles.

Answer:

2x

Step-by-step explanation:

7x= 7*x

5x=5*x

Subtract.

7-5=2

2*x=2x

So 2x is the answer.

Answer:

2x

Step-by-step explanation:

7x - 5x

Factor out x.

x ( 7 - 5 )

Subtract numbers.

x ( 2 )

Distribute x to 2.

2x

Answer:

After reflection, the coordinates would be A(-6,-8)  B(-2,-6)  C(-4,-2) and  D(-8,-4). After translation, the coordinates would be A(0,-8) B(4,-6)  C(2,-2)  and D(-2,-4).  

Step-by-step explanation:

If the figure ABCD consists of 4 points and we want to reflect this across the x-axis, then the y coordinate values of A, B, C and D will be negated. So,

(-6,8) becomes (-6,-8)

(-2,6) becomes (-2,-6)

(-4,2) becomes (-4,-2)

and (-8,4) becomes (-8,-4).

Now that we know what the reflection is, we translate it 6 units to the right. Therefore, the x value of each coordinate is increased by 6.

(-6,-8) becomes (0,-8)

(-2,-6) becomes (4,-6)

(-4,-2) becomes (2,-2)

and (-8,-4) becomes (-2,-4)

Hope this helped!

Answer:

here

alternate exterior angles--∠1, ∠8 and ∠2, ∠7

alternate interior angles--∠3, ∠6 and ∠4, ∠5

corresponding angles--∠1, ∠5 and ∠2, ∠6

vertical angles--∠2, ∠3 and ∠5, ∠8

Step-by-step explanation:

Answer:

here

alternate exterior angles--∠1, ∠8 and ∠2, ∠7

alternate interior angles--∠3, ∠6 and ∠4, ∠5

corresponding angles--∠1, ∠5 and ∠2, ∠6

vertical angles--∠2, ∠3 and ∠5, ∠8

Step-by-step explanation:

Answer:

Step-by-step explanation:

Length of an arc is expressed as [tex]L = \frac{\theta}{2\pi } * 2\pi r\\[/tex]. Given;

[tex]\theta = \frac{5\pi }{6} rad\\ radius = 24in\\[/tex]

The length of the minor arc SV is expressed as:

[tex]L = \frac{\frac{5\pi }{6} }{2\pi } * 2\pi (24)\\L = \frac{5\pi }{12\pi } * 48\pi \\L = \frac{5}{12} * 48\pi \\L = \frac{240\pi }{12} \\L = 20\pi \ in[/tex]

Hence, The length  of the arc SV is 20π in

Answer:

20 pi

Step-by-step explanation:

Answer:

19, 16, 20

Step-by-step explanation:

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.

Aka the highest number - the next highest number = lowest possible number.

3+4 is not greater than 8.

8 + 11 is not greater than 19.

5 + 5 is not greater than 11.

16+19 is greater than 20.

19+20 is greater than 16.

16+ 20 is greater than 19.

the set of numbers that could represent the lengths of the sides of a triangle is D. {19, 16, 20}.

To determine if a set of numbers can represent the lengths of the sides of a triangle, we need to apply the triangle inequality theorem. According to the theorem, for a triangle with side lengths a, b, and c:

a + b > c

a + c > b

b + c > a

Let's evaluate each set of numbers:

A. {3, 4, 8}

3 + 4 > 8 (7 > 8) - Not true

4 + 8 > 3 (12 > 3) - True

3 + 8 > 4 (11 > 4) - True

Since the first inequality is not true, set A cannot represent the lengths of the sides of a triangle.

B. {8, 11, 19}

8 + 11 > 19 (19 > 19) - Not true

8 + 19 > 11 (27 > 11) - True

11 + 19 > 8 (30 > 8) - True

Since the first inequality is not true, set B cannot represent the lengths of the sides of a triangle.

C. {11, 5, 5}

11 + 5 > 5 (16 > 5) - True

11 + 5 > 5 (16 > 5) - True

5 + 5 > 11 (10 > 11) - Not true

Since the third inequality is not true, set C cannot represent the lengths of the sides of a triangle.

D. {19, 16, 20}

19 + 16 > 20 (35 > 20) - True

19 + 20 > 16 (39 > 16) - True

16 + 20 > 19 (36 > 19) - True

All three inequalities are true for set D, so it can represent the lengths of the sides of a triangle.

Therefore, the set of numbers that could represent the lengths of the sides of a triangle is D. {19, 16, 20}.

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Answer:

(x + 8)² + (y - 3)² = 64

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (- 8, 3) and r = 8 , thus

(x - (- 8))² + (y - 3)² = 8² , that is

(x + 8)² + (y - 3)² = 64

Answer:

See below.

Step-by-step explanation:

The equation for a circle is:

[tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the center and r is the radius.

Plug in what we know. (-8,3) for (h,k) respectively and 8 for the radius:

[tex](x-(-8))^2+(y-(3))^2=(8)^2[/tex]

[tex](x+8)^2+(y-3)^2=64[/tex]

Answer:

  CPCTC

Step-by-step explanation:

Statements 3 and 4 show the top and bottom triangles are congruent, and the left and right triangles are congruent. Statement 5 is making use of these facts to claim that the alternate interior angles are congruent. This claim is valid because ...

  Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

Answer:

x=12.5

Step-by-step explanation:

0.7x times (-1.4)=-3.5

-0.28x=-3.5 (divide both sides)

Ans:12.5

Answer:

b = 12 sqrt(3)

Step-by-step explanation:

Since we have a right triangle we can use trig functions

cos theta = adjacent side / hypotenuse

cos 30 = b/c

cos 30 = b/24

24 cos 30 =b

24 * sqrt(3)/2 = b

12 sqrt(3) = b

Answer:

rhombus

Step-by-step explanation:

on edge

Answer: a. CI for the mean: 17.327 < μ < 26.473

b. CI for variance: 29.7532 ≤ [tex]\sigma^{2}[/tex] ≤ 170.9093

Step-by-step explanation:

a. To construct a 95% confidence interval for the mean:

The given data are:

mean = 21.9

s = 7.7

n = 12

df = 12 - 1 = 11

1 - α = 0.05

[tex]\frac{\alpha}{2}[/tex] = 0.025

t-score = [tex]t_{0.025,11}[/tex] = 2.2001

Note: since the sample population is less than 30, it is used a t-score.

The formula for interval:

mean ± [tex]t.\frac{s}{\sqrt{n} }[/tex]

Substituing values:

21.9 ± 2.200.[tex]\frac{7.7}{\sqrt{12} }[/tex]

21.9 ± 4.573

The interval is: 17.327 < μ < 26.473

b. A 95% confidence interval for the variance:

The given values are:

[tex]s^{2}[/tex] = [tex]7.7^{2}[/tex]

[tex]s^{2}[/tex] = 59.29

α = 0.05

[tex]\frac{\alpha}{2}[/tex] = 0.025

[tex]1-\frac{\alpha}{2}[/tex] = 0.975

[tex]\chi^{2}_{0.025,11}[/tex] = 21.92

[tex]\chi^{2}_{0.975,11}[/tex] = 3.816

Note: To find the values for [tex]\chi^{2}_{\alpha/2,n-1}[/tex] and [tex]\chi^{2}_{1-\alpha/2,n-1}[/tex], look for them at the chi-square table

The formula to calculate interval:

([tex]\frac{(n-1).s^{2}}{\chi^{2}_{\alpha/2,n-1}} , \frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2,n-1}}[/tex])

are the lower and upper limits, respectively.

Substituing values:

([tex]\frac{11.59.29}{21.92} , \frac{11.59.29}{3.816}[/tex])

(29.7532, 170.9093)

The interval for variance is: 29.7532 ≤ [tex]\sigma^{2}[/tex] ≤ 170.9093

Answer: MN represents the radius of the circle.

Step-by-step explanation:

The radius is the distance from the center to the outside of the circle.

Answer:

no

Step-by-step explanation:

f(g(x))= x if they are inverses

(x)=1/3x

g(x)= 1/3x

f(g(x)) = 1/3 (g(x) = 1/3 (1/3x) = 1/9x

This is not x so they are not inverse functions

Answer:

.7698

Step-by-step explanation:

Answer:

The depreciated value of the car after 1 yr is ​$16,353

The depreciated value of the car after 2 yr is ​$12,264.75

Step-by-step explanation:

Given

purchase amount P= $21,804

rate of depreciation R= 25%

applying the formula for the car deprecation we have

[tex]A= P*(1-\frac{R}{100} )^n[/tex]

Where,

A is the value of the car after n years,

P is the purchase amount,

R is the percentage rate of depreciation per annum,

n is the number of years after the purchase.

1. The depreciated value of the car after 1 yr is ​

n=1

[tex]A= 21,804*(1-\frac{25}{100} )^1\\\\A= 21,804*(1-0.25 )^1\\\\A= 21,804*0.75\\\\A= 16353[/tex]

The depreciated value of the car after 1 yr is ​$16,353

2. The depreciated value of the car after 2 yr is ​

n=2

[tex]A= 21,804*(1-\frac{25}{100} )^2\\\\A= 21,804*(1-0.25 )^2\\\\A= 21,804*0.75^2\\\\A= 21,804*0.5625\\\\A= 12264.75[/tex]

The depreciated value of the car after 2 yr is ​$12,264.75

Answer:

-6m+3

Step-by-step explanation:

Answer:

An equivalent value is -6m -n +3

Step-by-step explanation:

Given

-3(2m-1)-n   expand

=-6m+3-n

(also equals -6m -n +3 by commutativity)

Answer:

50.24 yd²

Step-by-step explanation:

pi r² = (3.14)(4)² = 50.24

Answer:

C and D

Step-by-step explanation:

khan acedemy

An equation is formed when two equal expressions. The solutions to the given equation are A, B, and C.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution of the given equation v²=25/81 can be found as shown below.

v²=25/81

Taking the square root of both sides of the equation,

√(v²) = √(25/81)

v = √(25/81)

v = √(5² / 9²)

v = ± 5/9

Hence, the solutions of the given equation are A, B, and C.

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Answer:

Step-by-step explanation:

The equivalent between sets is determined by the number of elements. If two sets have the same number of elements, then they are equivalent sets.

In this case, a year has 12 months, and the US has 50 states. So, one month is not equal to 1 state because they have different natures and they represent a different proportion. A month represents 1/12 of a year and a state represents 1/50 of the total number of states.

Answer:

0.007

Step-by-step explanation:

We were told in the above question that a random sample of 51 households is monitored for one year to determine aluminum usage

Step 1

We would have to find the sample standard deviation.

We use the formula = σ/√n

σ = 12.2 pounds

n = number of house holds = 51

= 12.2/√51

Sample Standard deviation = 1.7083417025.

Step 2

We find the z score for when the sample mean is more than 61

z-score formula is z = (x-μ)/σ

where:

x = raw score = 61 pounds

μ = the population mean = 56.8 pounds

σ = the sample standard deviation = 1.7083417025

z = (x-μ)/σ

z = (61 - 56.8)/ 1.7083417025

z = 2.45852

Finding the Probability using the z score table

P(z = 2.45852) = 0.99302

P(x>61) = 1 - P(z = 2.45852) = 0.0069755

≈ 0.007

Therefore,the probability that the sample mean will be more than 61 pounds is 0.007

Answer:

perimeter = 12 miles

area = 6 square miles

Step-by-step explanation:

Since it makes a right triangle, use the Pythagorean Formula.

3^2+4^2=c^2

9+16=c^2

25=c^2

5=c, so the hypotenuse of the right triangle is 5.

Perimeter = 3+4+5 = 12 miles

area = 1/2bh (1/2 base times height)

=1/2x3x4

=6

Area = 6 square miles

Answer:

7/3 or 13/15

Step-by-step explanation:

So you told me that it will be

8/(20/9) -2 11/15 I put parenthesis to make it easier to understand for me

so you must know that a/(b/c)=ac/b si

72/20 -2 11/15 so we work with -2 11/15 which is equal to -30/15 + 11/15 and that will be -19/15 so we have

72/20 - 19/15 we simplify

18/5 - 19/15 so we multiply and divide by 3 in 18/5

54/15 - 19/15 and we add up

35/15 which is equal to

7/3

If this is wrong so we work with -2 11/15 which is equal to -30/15 + 11/15 well it should be so we work with -2 11/15 which is equal to -30/15 - 11/15 and  that equals -41/15 and we get

54/15-41/15

13/15

Answer:

[tex]L(x)=4-x[/tex]

[tex]L(3.9)=0.1\\L(3.99)=0.01[/tex]

Step-by-step explanation:

The linear approximating polynomial is: [tex]L(x) = f(a) + f'(a)(x - a)[/tex]

Given: [tex]f(x) = 4 - x[/tex] at a=0

f(0)=4-0=4

f'(x)=-1, Therefore: f'(a)=-1

Therefore, the linear approximation of f(x) at a=0 is:

[tex]L(x) = f(0) + f'(a)(x - 0)\\L(x)=4-x[/tex]

We then use our result to approximate 3.9 and 3.99.

[tex]L(3.9)=4-3.9=0.1\\L(3.99)=4-3.99=0.01[/tex]

Answer:

it we'll be 0.3

Step-by-step explanation:

trust me man I like to explain but it's long

Answer:

0.3 meter or 3/10 meter

Step-by-step explanation:

As there are 100cm in 1 meter and you want to find 30cm in terms of meters.

It will be as

100cm = 1 meter     (rule/lax)

100/100 cm = 1/100  meter   (divide both sides of equation with 100)

1 cm = 1/100 meter

1 *30 cm = (1/100)*30  meter    (multiply both sides with 30)

30 cm = 30/100 meter

30/100 more shortly can be written as  3/10 meter or in decimals 0.3 meter.

Answer:

a. 0.34885

b. 0.04651

c. 0.02404

d. 36

e. 14.7, say 15 trials

Step-by-step explanation:

Q17070205

Note:  

1. In order to be applicable to established probability distributions, each roll is considered a Bernouilli trial, i.e. has only two outcomes, success or failure, and are all independent of each other.

2. use R to find the probability values from the respective distributions.

a) the chance that the first 6 appears before the tenth roll

This means that a six appears exactly once between the first and the nineth roll.

Using binomial distribution, p=1/6, n=9, x=1

dbinom(1,9,1/6) = 0.34885

b) the chance that the third 6 appears on the tenth roll

This means exactly two six's appear between the first and 9th rolls, and the tenth roll is a six.

Again, we have a binomial distribution of p=1/6, n=9, x=2

p1 = dbinom(2,9,1/6) = 0.27908

The probability of the tenth roll being a 6 is, evidently, p2 = 1/6.

Thus the probability of both happening, by the multiplication rule, assuming independence  

P(third on the tenth roll) = p1*p2 = 0.04651

c) the chance of seeing three 6's among the first ten rolls given that there were six 6's among the first twenty roles.

Again, using binomial distribution, probability of 3-6's in the first 10 rolls,

p1 = dbinom(3,10,1/6) = 0.15504

Probability of 3-6's in the NEXT 10 rolls

p1 = dbinom(3,10,1/6) = 0.15504

Probability of both happening  (multiplication rule, assuming both events are independent)

= p1 *  p1 = 0.02404

d) the expected number of rolls until six 6's appear

Using the negative binomial distribution, the expected number of failures before n=6 successes, with probability p = 1/6

=  n(1-p)/p

Total number of rolls by adding n  

= n(1-p)/p + n = n(1-p+p)/p = n/p = 6/(1/6) = 36

e) the expected number of rolls until all six faces appear

P1 = 6/6 because the firs trial (roll) can be any face with probability 1

P2 = 6/5 because the second trial for a different face has probability 5/6, so requires 6/5 trials

P3 = 6/4 ...

P4 = 6/3

P5 = 6/2

P6 = 6/1

So the total mean (expected) number of trials is 6/6+6/5+6/4+6/3+6/2+6/1 = 14.7, say 15 trials

Answer:

y ≤ 3x − 1, y ≤ −x + 4

Step-by-step explanation:

The line f(x) is solid and goes through the points (0, 4) and (4, 0) and is shaded below the line.

The line that satisfies the point (0,4) and (4,0) is y=-x+4

Since it is shaded below the line, we have the inequality sign: [tex]\leq[/tex]

Therefore, one of the lines is: [tex]y\leq -x+4[/tex]

The line g(x) is solid and goes through the points (0, -1) and (2, 5) and is shaded below the line.

Slope, [tex]m=\frac{5-(-1)}{2-0}=3[/tex]

When x=0, y=-1

y=mx+b

y=3x+b

-1=3(0)+b

b=-1

Therefore, the equation of the line is: [tex]y=3x-1[/tex]

Since it is shaded below the line, we have the inequality sign: [tex]\leq[/tex]

Therefore, the other line is: [tex]y\leq 3x-1[/tex]

An inequality is a comparison between two expressions not based on equality

The graph represents the system of the inequalities; y ≤ 3·x - 1, y ≤ -x + 4

Reason:

The given parameters are;

Points on the line f(x) = (0, 4), (4, 0)

[tex]Slope \ of \ the \ line, \ m =\dfrac{4-0}{0-4} = -1[/tex]

Therefore;

The equation of the line is y - 0 = -1·(x - 4), which gives;

y = -x + 4

The inequality representing the line is y ≤ -x + 4

Points on the line g(x) = (0, -1), (2, 5)

[tex]Slope \ of \ the \ line, \ m =\dfrac{-1-5}{0-2} = \dfrac{-6}{-3} =3[/tex]

Equation of the line is y - (-1) = 3·(x - 0)

∴ y = 3·x - 1

The inequality is y ≤ 3·x - 1,

The graph which represent the system of inequalities are;

y ≤ 3·x - 1, y ≤ -x + 4

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Answer:

KU = 8

Step-by-step explanation:

From the diagram

KU + UN = KN , that is

KU + 40 = 48 ( subtract 40 from both sides )

KU = 8

Answer:

KU = 8

Step-by-step explanation:

UN = 40

        KN = 48

KU + UN = 48

 KU + 40 = 48  {Subtract 40 from both sides}

         KU = 48 -40

         KU = 8

Answer:

a. 73; b. 48.9; c. 2; d. 33.8; e. 73

Step-by-step explanation:

Assume the function was

S(t)= 73 - 15 ln(t + 1), t  ≥ 0

a. Average score at t = 0

S(0) = 73 - 15 ln(0 + 1) = 73 - 15 ln(1) = 73 - 15(0) =73 - 0 = 73

b. Average score at t = 4

S(4) = 73 - 15 ln(4 + 1) = 73 - 15 ln(5) = 73 - 15(1.61) =73 - 24.14 = 48.9

c. Average score at t =24

S(24) = 73 - 15 ln(24 + 1) = 73 - 15 ln(25) = 73 - 15(3.22) =73 - 48.28 = 24.7

d. Percent of answers retained

At t = 0. the students retained 73 % of the answers.

At t = 24, they retained 24.7 % of the answers.

[tex]\text{Percent retention} = \dfrac{\text{24.7}}{\text{73}} \times 100 \, \% = \text{33.8 \%}\\\\\text{The students retained $\large \boxed{\mathbf{33.8 \, \%}}$ of their original knowledge after two years.}[/tex]

e. Maximum of the function

The maximum of the function is at t= 0.

Max = 73 %

The graph below shows your knowledge decay curve. Knowledge decays rapidly at first but slows as time goes on.

Answer:

Increasing: [tex](0, 750)[/tex]

Decreasing: [tex](750, \infty)[/tex]

Step-by-step explanation:

Critical points:

The critical points of a function f(x) are the values of x for which:

[tex]f'(x) = 0[/tex]

For any value of x, if f'(x) > 0, the function is increasing. Otherwise, if f'(x) < 0, the function is decreasing.

The critical points help us find these intervals.

In this question:

[tex]P(x) = -0.004x^{2} + 6x - 5000[/tex]

So

[tex]P'(x) = -0.008x + 6[/tex]

Critical point:

[tex]P'(x) = 0[/tex]

[tex]-0.008x + 6 = 0[/tex]

[tex]0.008x = 6[/tex]

[tex]x = \frac{6}{0.008}[/tex]

[tex]x = 750[/tex]

We have two intervals:

(0, 750) and [tex](750, \infty)[/tex]

(0, 750)

Will find P'(x) when x = 1

[tex]P'(x) = -0.008x + 6 = -0.008*1 + 6 = 5.992[/tex]

Positive, so increasing.

Interval [tex](750, \infty)[/tex]

Will find P'(x) when x = 800

[tex]P'(x) = -0.008x + 6 = -0.008*800 + 6 = -0.4[/tex]

Negative, then decreasing.

Answer:

Increasing: [tex](0, 750)[/tex]

Decreasing: [tex](750, \infty)[/tex]

The required 90% confidence interval for adult males is

[tex]\text {CI} = (64.2, \: 70.6)\\\\[/tex]

The required 90% confidence interval for adult females is

[tex]\text {CI} = (72, \: 79.2)\\\\[/tex]

The confidence interval of male and female pulse rates do not overlap since the mean pulse rate of female is way greater than the mean pulse rate of males.

Step-by-step explanation:

We are given the pulse rates of adult females and adult males and we have to construct the 90% confidence interval of the mean pulse rate for males and females.

Let us first compute the mean and standard deviation of the given pulse rates data.

Using Excel,  

=AVERAGE(number1, number2,....)  

The mean pulse rate of adult males is found to be

[tex]\bar{x}_{male} = 67.4[/tex]

The mean pulse rate of adult females is found to be

[tex]\bar{x}_{female} = 75.6[/tex]

Using Excel,  

=STDEV(number1, number2,....)    

The standard deviation for adult male pulse rate is found to be

 [tex]s_{male} = 11.9[/tex]

The standard deviation for adult female pulse rate is found to be  

 [tex]s_{female} = 13.5[/tex]

The confidence interval is given by

[tex]$ \text {CI} = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $\\\\[/tex]

Where [tex]\bar{x}[/tex] is the sample mean, n is the sample size, s is the sample standard deviation and   [tex]t_{\alpha/2}[/tex] is the t-score corresponding to a 90% confidence level.  

The t-score corresponding to a 90% confidence level is  

Significance level = α = 1 - 0.90 = 0.10/2 = 0.05  

Degree of freedom = n - 1 = 40 - 1 = 39

From the t-table at α = 0.05 and DoF = 39

t-score =  1.685

The required 90% confidence interval for adult males is

[tex]\text {CI} = 67.4 \pm 1.685\cdot \frac{11.9}{\sqrt{40} } \\\\\text {CI} = 67.4 \pm 1.685\cdot 1.882\\\\\text {CI} = 67.4 \pm 3.17\\\\\text {CI} = 67.4 - 3.17, \: 67.4 + 3.17\\\\\text {CI} = (64.2, \: 70.6)\\\\[/tex]

Therefore, we are 90% confident that the actual mean pulse rate of adult male is within the range of 64.2 to 70.6 bpm

The required 90% confidence interval for adult females is

[tex]\text {CI} = 75.6 \pm 1.685\cdot \frac{13.5}{\sqrt{40} } \\\\\text {CI} = 75.6 \pm 1.685\cdot 2.1345\\\\\text {CI} = 75.6 \pm 3.60\\\\\text {CI} = 75.6 - 3.60, \: 75.6 + 3.60\\\\\text {CI} = (72, \: 79.2)\\\\[/tex]

Therefore, we are 90% confident that the actual mean pulse rate of adult female is within the range of 72 to 79.2 bpm

Comparison:

The confidence interval of male and female pulse rates do not overlap since the mean pulse rate of female is way greater than the mean pulse rate of males.