Two bikers meet at a park. Biker A needs to stop at the store that is 12 miles east of the park. Biker B heads southeast at a 61° angle at the same time for 24 miles. Once biker A leaves the store he heads southwest at an angle of 89° for 21 miles. Do NOT use the law of cosines, use your knowledge from the content of this course.

a. Use your knowledge of triangles to figure out if the two bikers will be able to meet up if each biker travels the distance given.
b. If they do not meet up, how much farther would one of the bikers have to travel to meet the other?
c. What is the measure of the angle between the bikers?
d. What is the relationship between the measure of the angles and the paths the bikers took?
e. Classify the triangle the paths created.
f. How many miles did they travel together?

Answer:

56.57 rounded to the nearest hundredths

Step-by-step explanation:

a^2 + b^2  =  c^2

20^2 + x^2 = 60^2

400 to x^2 = 3600

x^2 = 3200 take the square root of each side.

x = 56.57 rounded to the nearest hundredths

The minimum cost for this spanning tree has been calculated as $1100.

This is solves as

AC + CD + DF + FE + EB

This would be

15 + 25+ 23 + 22 + 25

= 110

The minimum cost would be gotten by multiplying this valus with the amount per foot

= 10 * 110

= $1100

Hence the minimum cost of the spanning tree is $1100

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20. A rational function [tex]\frac{p(x)}{q(x)}[/tex] (where [tex]p,q[/tex] are polynomials in [tex]x[/tex]) has a removable discontinuity at [tex]x=a[/tex] if for some positive integer [tex]n[/tex] we can factorize

[tex]p(x) = (x-a)^n p^*(x)[/tex]

[tex]q(x) = (x-a)^n q^*(x)[/tex]

[tex]\implies \dfrac{p(x)}{q(x)} = \dfrac{(x-a)^n p^*(x)}{(x-a)^n q^*(x)} = \dfrac{p^*(x)}{q^*(x)}[/tex]

That is, we "remove" the discontinuity at [tex]x=a[/tex] because while [tex]x\neq a[/tex], we have [tex]\frac{x-a}{x-a}=1[/tex]. The discontinuity is still there, since [tex]\frac{p(a)}{q(a)}[/tex] is undefined, but in the limit sense we can essentially ignore the factors of [tex]x-a[/tex]. The graph of [tex]\frac{p(x)}{q(x)}[/tex] will have all the features of [tex]\frac{p^*(x)}{q^*(x)}[/tex] aside from a hole at [tex]x=a[/tex].

In this case, we have

[tex]f(x) = \dfrac{x+4}{x^2-x-20} = \dfrac{x+4}{(x+4)(x-5)}[/tex]

and when [tex]x\neq-4[/tex], we can cancel the factor of [tex]x+4[/tex] so that

[tex]f(x) = \begin{cases}\dfrac1{x-5} & \text{if }x \neq -4 \\\\ \text{DNE} & \text{if }x = -4\end{cases}[/tex]

("DNE" = "does not exist", i.e. is undefined. For some reason "undefined" wouldn't render...)

This means [tex]x=-4[/tex] is a removable discontinuity.

We cannot do the same with the factor of [tex]x-5[/tex], so in contrast [tex]x=5[/tex] is a non-removable discontinuity.

21. The pieces of [tex]f(x)[/tex] defined on [tex]x<2[/tex] and [tex]x>2[/tex] are themselves continuous since they are polynomials. Then the continuity of [tex]f(x)[/tex] over the entire real line depends on the point where the pieces meet.

Here we have

[tex]f(x) = \begin{cases}x+3 & \text{if }x\le2 \\ cx+6 & \text{if }x>2\end{cases}[/tex]

so the pieces meet at [tex]x=2[/tex]. Continuity at this point requires that the both limits from either side of [tex]x=2[/tex] be the same. This means

[tex]\displaystyle \lim_{x\to2^-} f(x) = \lim_{x\to2} (x+3) = 2+3 = 5[/tex]

[tex]\displaystyle \lim_{x\to2^+} f(x) = \lim_{x\to2} (cx+6) = 2c + 6[/tex]

Solve for [tex]c[/tex].

[tex]2c + 6 = 5 \implies 2c = -1 \implies \boxed{c = -\dfrac12}[/tex]

Answer:

solution

Given,

70 kg rice =Rs.5600

1 kg= Rs5600÷70

=Rs.80

Rs.80 is for per kg.

For 1 quintal

1 quintal=100 kg

Then,

100×80

=Rs.8000.

Answer:

Step-by-step explanation:

Answer:

the tip should be 9 dollars

Step-by-step explanation:

Answer:

1.1%

Step-by-step explanation:

To convert from percentage to decimal you simply divide by 100 so to convert from decimal to percentage you do the opposite, by multiplying by 11. In doing so, you get 1.1%. Think about it this way, if you wanted 100% of an item, you would basically just be multiplying by 1... which is 100% divided by 100. But if you wanted 50%, you would want half, or other in other words divide it in half, which is the same as multiplying by 0.50 which is 50% divided by 100

Answer:

The numbers between 8 and 8

9 is 8.5

8, 8.5, 9

Renting a car on a monthly basis after 19 days makes it cheaper than renting on a daily basis.

How to solve such questions?

The key concept for solving such questions is by calculating the number of days on which both renting a car on a monthly basis equals renting a car on daily basis. So on the very next day as renting a car on daily basis still adds up the expense it will become costlier and renting a car on monthly basis makes it cheaper.

Given:-

Cost of renting car on a daily basis = $40

Cost of renting car on a monthly basis = $750

Let number of days on which both renting a car on a monthly basis equals renting a car on daily basis be x.

Therefore

40 × x = 750

x =  [tex]\frac{750}{40}[/tex]

x = 18.75 days

From 19th day onwards cost of renting on a daily basis will exceed cost of renting car on a monthly basis.

Thus , Renting a car on a monthly basis after 19 days makes it cheaper than renting on a daily basis.

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The volume of the box is 99 unit cubes.

A cube is a three-dimensional object that has six faces, twelve edges and eight vertices. The length, width and height of a cube usually has equal dimensions. The volume of the box is a function of the dimension of the cubes in it and the number of layers.

Volume of a box = number of layers x amount of units

9 x 11 - 99 unit cubes

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Given: the number is less than 20; three-factor pairs; each factor pair individually adds up to 19, 11, and 9

Solve for her number.

Step-by-step explanation:

If you think about it for a little bit, you will eventually find that 18 + 1 = 19 and 18 × 1 = 18 which is less than 20.

Then we know 18 has 2 more factor pairs : 9 × 2 and 6 × 3 which add up to 11 and 9.

Therefore our answer is: 18

18 × 1

9 × 2

6 × 3

The trick is to pick the largest sum of one-factor pair (19 in this question) and then choose the number below it.

Supposing that 20 out of 100 people choose black or gray, the percentage is of 20%.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

Hence, if 20 out of 100 people choose black or gray, the percentage is given by:

[tex]P = \frac{20}{100} \times 100\% = 20\%[/tex]

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Answer:

(A, B, C, D)

What is the sample space of the probability?

Sample space is the set of all possible outcomes of a random experiment.

Here given possible outcomes are A, B, C, D

Hence, Sample space of probability = (A, B, C, D), total 4 different choices

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Answer :

The set of all possible out in a random experiment is refer to as sample space.

The reading above is an example of discrete(finite) sample space.

Following the Discrete Probability Law if a sample space consist of a finite number ex:{1 ,2 ,3} . The probability is the sum of the probabilities of the elements.

Therefore answering a multiple choice questions with A,B,C and D are four choices with possible answer of A,B,C and D.

Answer:

it's a sin

chsheuheheuehhehrhrhrhr

The relationship between ∠E and ∠K is  ∠E = ∠K

Two lines are said to be parallel when they do not meet even at infinity and the distance between them always remains constant.

∠E = ∠G   ( vertical angles) ∠H = ∠F   ( vertical angles) ∠G = ∠K  (corresponding angles) From equations i) and iii)

we get ∠E  = ∠K and they are alternate exterior angles.

The measure of angle K can be found from the equation

 ∠K + ∠J = 180°    (consecutive interior angles)

∠K = 180° - ∠J

∠K + ∠L = 180°

∠K = 180° - ∠L

The missing image is attached with the answer.

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Answer:

ABCDE is a regular pentagon with congruent diagonals BE and BD. a) Justify AABE = ACBD with a test for congruent triangles. b) Name a pair of congruent quadrilaterals.

The present age of Madison is 1027 years and that of his mother is 3080 years (rounded off to nearest whole numbers), solved using the linear equation in one variable: (x + 614) + (3x + 614) = 5334, where x represents the present age of Madison.

Linear equations in one variable are the linear relationship between two algebraic expressions not involving more than one variable throughout the equation.

In the question, we are informed that the present age of Maison's mother is 3 times that of Madison. After 614 years, the sum of their age will be 5334 years.

We are asked to determine their present ages.

We assume the present age of Madison to be x years.

Therefore, the present age of Madison's mother = 3x years {3 times that of Madison}.

Now, after 614 years, both of their ages will increase by 614 years.

Therefore, age of Madison after 614 years = x + 614 {Present + 614}.

Age of Madison's mother = 3x + 614 {Present + 614}.

We are given that after 614 years, the sum of their ages will be 5334.

This can be represented by the linear equation in one variable:

(x + 614) + (3x + 614) = 5334

This linear equation in one variable can be simplified and solved in the following way:

or, 4x + 1228 = 5334 {Simplifying},

or, 4x + 1228 - 1228 = 5334 - 1228 {Subtracting 1228 from both sides}

or, 4x = 4106 {Simplifying}

or, 4x/4 = 4106/4 {Dividing both sides by 4},

or, x = 1026.5 {Simplifying}.

Therefore, the present age of Madison = x = 1026.5 = 1027 years (nearest whole number).

The present age of Madison's mother = 3x = 3*1026.5 = 3079.5 = 3080 years (nearest whole number).

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Answer:

x = 39°

y = 90°

Step-by-step explanation:

Answer:

x = 39°

y = 92°

Step-by-step explanation:

x = 39° because alternate (or z) angles are equal.

x = 92° because all angles in a triangle add up to 180°.

so

49+39=88

angles on a straight line are equal to 180°

180°-88° = 92

Hope this helps!

Anja’s phrase should have ended with “less than –15”, not “at least –15”.

Given statement:

Anja represents the inequality (4-g)/8 <-15

With the phrase “the quotient of the difference of 4 and a number and 8 is at least –15.”

Let the number be g.

“the quotient of the difference of 4 and a number and 8" translated to (4-g/8)

"at least" means : <

“the quotient of the difference of 4 and a number and 8 is at least –15.” translated to (4-g)/8 <-15

Therefore, Anja’s phrase should have ended with “less than –15”, not “at least –15”.

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There are 362,880 ways that members of this group can gather.

A permutation is an act of arranging items or elements in the correct order.

Amie, Bruce, Corey, Dwayne, Eric, Frank, Georgia, Helen and Isis, members of an architectural firm, plan to meet in the company conference room to discuss the project coordinator's plans for their next project.

Denote these nine people by A, B, C, D, E, F, G, H, and I.

Then the total number of ways that members of this group can gather will be

⇒ 9!

⇒ 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

⇒ 362,880

There are 362,880 ways that members of this group can gather.

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Answer:

linear

Step-by-step explanation:

From the table, we can deduct that y = 1.3x, which means it is a linear function. A linear function, when graphed, is a straight line.

Options A and D are having a slope equal to -3/5.

Given that the slope of the line is -3/5.

That is, m = -3/5

We need to find which ordered pairs could be points on a parallel line.

The formula for slope between two coordinates is m = (y₂ - y₁)/(x₂ - x₁).

Now,

Using (–8, 8) and (2, 2);

m = (2 - 8)/(2 - (-8))

⇒m = -6/10

⇒m = -3/5

Using (–5, –1) and (0, 2);

m = (2 - (-1))/(0 - (-5))

⇒m = 3/5

Using (–3, 6) and (6, –9);

m = (-9 - 6)/(6 - (-3))

⇒m = -15/9

⇒m = -5/3

Using (–2, 1) and (3, –2);

⇒m = (-2 - 1)/(3 - (-2))

⇒m = -3/5

Using (0, 2) and (5, 5);

m = (5 - 2)/(5 - 0)

⇒m = 3/5

We know that the condition for parallel lines slope is [tex]m_{1} =m_{2}[/tex].

Therefore, options A and D are having a slope equal to -3/5.

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x = 39 degrees

(alternate angles)

Angles in triangle = 180

49 + 39 = 88

So, the missing angle inside the triangle is 92

Angles on straight line = 180

180 - 92 = 88

y = 88 degrees

Hope this helps!

Answer:

  C, E, D

Step-by-step explanation:

A "unit rate" is a rate that has 1 unit in the denominator. Here, the rates are all given in terms of the number of apples in 1 basket. (The 1 basket is the 1 unit.)

When rates are given with some number of units other than 1 in the denominator, divide the numerator by the denominator to find the unit rate.

Here, the unit rates are all more than one apple in each basket, so the number of apples must be a multiple of the number of baskets. Phrases "A" and "B" both have more baskets than apples, so will not be used.

  C: (304 apples)/(8 baskets) = (304/8) apples/basket = 38 apples/basket

  D: (294 apples)/(7 baskets) = (294/7) apples/basket = 42 apples/basket

  E: (405 apples)/(9 baskets) = (405/9) apples/basket = 45 apples/basket

  (38 apples)/(1 basket) = C: 38 apples/basket

  (45 apples)/(1 basket) = E: 45 apples/basket

  (42 apples)/(1 basket) = D: 42 apples/basket

The correct difference between the expressions is 4z⁵. The correct option is the first option 4z⁵

From the question, we are to simplify the given expression by subtracting the expressions

The given expression is

-3z⁵ - (-7z⁵)

Clear the parenthesis by multiplying

-3z⁵ +7z⁵

Simplifying

4z⁵

The simplified form of the expression is 4z⁵

Hence, the correct difference between the expressions is 4z⁵. The correct option is the first option 4z⁵

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Answer:

Step-by-step explanation:

The surface area of the solid formed is approximately, 598.3 in².

Surface area of the solid is the area covered by the solid all round.

The given parameters are:

Surface area of the solid formed = 5(10×10) + (0.5×10×8.67) + 3(10×1.83) = 598.3 in²

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Answer:

a gap analysis is a method of assessing the performance of a business unit to determine whether business requirements order objectives are being met and if not what steps should be taken me them a gap analyse may also be referred to as need analysis need assessment or need gap analysis

Answer:

16 I can't find the lengths but Angle A = Angle B = Angle C = 60 degrees.

17 X = 55 degrees, Y = 60 degrees, Z = 65 degrees.

18 Angle B and Angle C

19 BC and AC

20 They are all 60 degrees and are all equal to each other.

Hope I helped!

The population standard deviation is the standard deviation of the whole population denoted by sigma.

The sample mean is denoted by x bar and standard deviation by sx and it is the mean and standard deviation of the sample not the population from which the sample is chosen.

The data given in problem answers the first part.

The mean weight  of the sample denoted by  x bar x ¯ was two ounces with a standard deviation denoted by sx of 0.12 ounces.

The population standard deviation is denoted by σ known to be 0.1 ounce.

a. i. x ¯ =___2_____ ii. σ =___0.1_____ iii. sx =___0.12_____

e. Sub part i) 1.959 ; 2.041

Sub part iii) The error bound is 0.041

f. Sub Part i) 1.935 ; 2.065

Sub Part iii) The error bound is 0.0645

Part b)

The random variable X  is any number defining the weights of the  sample chosen from the population.

Part c)

The random variable X bar is the average weight of the sample obtained by adding the total weights of the sample divided by the number of the sample size.

Part d)

The normal distribution is used to solve the problem because the sample size is less than 30.

Part e

The 90 % confidence interval is calculated as ∝ = 1- 90%

∝ = 0.1

∝/2= 0.1/2= 0.05

xbar± z(∝/2) σ /√n

Putting the values

2± 1.645 (0.1)/√16

2± 0.041

or

Sub part i) 1.959 ; 2.041

Sub part iii) The error bound is 0.041

Part f

The 98 % confidence interval is calculated as ∝ = 1- 98%

∝ = 0.02

∝/2= 0.1/2= 0.01

xbar± z(∝/2) σ /√n

Putting the values

2± 2.58 (0.1)/√16

2± 0.0645

or

Sub Part i) 1.935 ; 2.065

Sub Part iii) The error bound is 0.0645

Part g

The confidence interval in part f is larger than the confidence interval in part e because we are 98 percent confident about the accuracy of the result. The interval is 0.01 for two tailed test which is very less as compared to 0.05 for 90% confidence interval.

The larger the area of the confidence interval less sure we are about the accuracy of the result hence getting a smaller value .

Part h

On the average 90 % of the 16 sample will have the true value of the mean.

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