). Bees are one of the fastest insects on Earth. They can fly 22 miles in 2 hours, and 55 miles in 5 hours. Write an algebraic expression to show how many miles a bee can fly in h hours. If a bee flies 4 hours at this speed, how many miles will it travel?

Answer:

She makes 7.8% portion of sales collectively.

Step-by-step explanation:

Let us assume she makes total of 100 calls.

The percentage of calls which are busy or unanswered = 22 %

So, now calculating 22% of 100 , we get:

[tex]\frac{22}{100} \times 100 = 22[/tex]

So, 22 of her calls are UNANSWERED.

Now, let us find out the number of calls successfully made by telemarketer.

Total successful calls = Total Calls made - Number of unanswered calls

                                    = 100 - 22  = 78

So, she makes a total of 78 calls successfully.

Now, he sells subscriptions to 10% of the 78 calls made successfully.

So, now calculating 10% of 78 , we get:

[tex]\frac{10}{100} \times 78 = 7.8[/tex]

So, she sold 7.8 subscriptions in total out of 100 attempts.

Also, as we know 7.8 out of 100  = 7.8% of 100.

Hence, she makes 7.8% portion of sales collectively.

Final answer:

To find the time it will take for an object to travel a certain distance at a given speed, divide the distance by the speed. The estimated time to travel 4.9 km at a speed of 10 km/h is approximately 0.5 hours. The exact time, considering the speed as 10.1 km/h, is also approximately 0.5 hours.

Explanation:

To find the time it will take for an object to travel a certain distance at a given speed, we can use the formula:

Time (in hours) = Distance (in kilometers) / Speed (in kilometers per hour)

First, let's round the speed to the nearest integer, which is 10 km/h. To estimate the time it will take to travel 4.9 km, we can divide the distance by the estimated speed:

Estimated Time = 4.9 km / 10 km/h ≈ 0.49 hours ≈ 0.5 hours

To find the exact time, we will use the given speed of 10 and one-tenth km/h. We can convert this speed to decimal form, which is 10.1 km/h. Now, we can calculate the exact time:

Exact Time = 4.9 km / 10.1 km/h ≈ 0.485 hours ≈ 0.5 hours

Therefore, it will take approximately 0.5 hours or 30 minutes for the object to travel 4.9 km.

Answer: There are 15 nickles and 20 dimes.

Step-by-step explanation:

Since we have given that

Let the number of nickles be 'x'

Let the number of dimes be '2x-10'.

Total amount = $2.75

According to question, we get that

[tex]0.1(2x-10)+0.05x=2.75\\\\0.2x-1+0.05x=2.75\\\\0.25x=2.75+1\\\\0.25x=3.75\\\\x=\dfrac{3.75}{0.25}\\\\x=15[/tex]

Hence, there are 15 nickles and [tex]2x-10=2(15)-10=30-10=20[/tex] dimes.

Therefore, there are 15 nickles and 20 dimes.

Final answer:

Mary has 15 nickels and 20 dimes.

Explanation:

Let's solve this problem step-by-step:

Answer:

e) Trend Analysis

The term is 'trend analysis'. This refers to a statistical method used to evaluate and predict future trends based on historical data. This technique is specifically referenced in prediction of labor demand using prior year’s data.

The concept referred to in the question is e. Trend analysis. Trend analysis is a statistical method used to evaluate and predict future trends based on historical data. In the context of labor demand, a trend analysis would involve examining labor demand data from the previous year, identifying patterns and trends within that data, and using statistical models to make predictions about labor demand for the upcoming year.

For example, suppose a company has seen a steady increase in labor demand over the past five years. Based on this trend, they can build a statistical model that predicts an increase in labor demand for the next year as well. This strategy helps companies plan for their future staffing needs, ensuring they have the necessary resources to meet their objectives.

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Answer:

  see below

Step-by-step explanation:

As always, the coordinate transformations are ...

  a. 180° — (x, y) ⇒ (-x, -y)

  b. 270° CCW or 90° CW — (x, y) ⇒ (y, -x)

  c. 90° CCW or 270° CW — (x, y) ⇒ (-y, x)

___

It can be quick and easy to use a transparency or tracing paper to locate the rotated position of the image.

Answer:

More. The product of 25 and 3/5 is 15 which is greater than 14.

Step-by-step explanation:

The amount paid by Heron for the video game  is $46.64.

Step-by-step explanation:

Here, the marked price of the video game  = $55

The discount percentage on the video game  = 20%

Calculating 20% of the $55, we get:

[tex]\frac{20}{100} \times 55 = 11[/tex]

So, the discount offered on the video game  = $11

Selling Price  = Marked Price  - Discount

                        =$55 - $11 = $44

Now,  the tax percentage on the video game  = 6%

Calculating 6% of the $44, we get:

[tex]\frac{6}{100} \times 44 =2.64[/tex]

So, the tax  on the video game  = $2.64

New Selling Price  = Selling Price  +  Tax

                        =$44 + $2.64  = $46.64

So, the amount paid by Heron for the video game  is $46.64.

Answer:

  -8

Step-by-step explanation:

Let n represent the number. Then we have ...

  n -3 . . . . the difference of a number and 3

  = . . . . . .  equals

  5 +2n . . . 5 added to twice the number

Adding -n-5 to both sides of the equation gives ...

  n -3 -n -5 = 5 +2n -n -5

  -8 = n . . . . . simplify

The number is -8.

Answer:

The distance is 6.3 units

Answer: [tex]\frac{2}{4}[/tex]  or [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

You need to analize the information given in the exercise.

Let be "x" represents the whole distance part that Jolene have driven to the state park.

According the the explained in the problem, in the first day Jolene drove [tex]\frac{1}{4}[/tex] of the distance.

 Knowing that, you can identify that the whole distance (or the value of "x"), is the following:

[tex]x=\frac{4}{4}[/tex]    

(If you simplify it, you get: [tex]x=1[/tex])

You also know that the second day Jolene drove farther than the first day; therefore, there are two possible cases for the part of the distance she might have driven the second day.  These cases are:

Case 1: [tex]\frac{2}{4}[/tex] of the distance the second day.

Case 2: [tex]\frac{3}{4}[/tex] of the distance the second day.

Answer: The volume is 143

Step-by-step explanation:

Modular division, also known as modular arithmetic, has various applications in cryptography, computer science, and number theory. It is used in encryption algorithms like RSA and in solving congruence equations.

Modular division, also known as modular arithmetic, is a mathematical operation that involves finding the remainder when one number is divided by another. Modular division is commonly used in various mathematical applications such as cryptography, computer science, and number theory.

One application of modular division is in the encryption and decryption of data using modular arithmetic. For example, the RSA encryption algorithm relies on modular division to encode and decode messages.

Another application of modular division is in solving congruence equations. Congruence equations represent the idea of equivalence of numbers modulo a given number. By using modular division, we can determine the solutions to these equations.

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Modular division is used to find remainders in mathematics, but it is not used for dividing polynomials or dividing by zero. It's also not useful for dividing vectors in physics.

Modular division is a mathematical method used to find the remainder of a division problem, but it is not necessarily applicable in all contexts. For example, dividing a polynomial by a polynomial generally does not result in a polynomial, indicating that other methods must be used in this situation. Furthermore, it's important to note that modular division cannot be used to divide by zero, since this is undefined in mathematics. Additionally, within the discipline of physics, modular division is not applicable for operations such as dividing a vector by another vector component by component, as there are no useful physics applications for this type of operation.

Answer:

Step-by-step explanation:

The relationship is negative, negative correlation

Answer:

(a) V(0) = 50 gal, V(20) = 0 gal

(b)At t= 0 the tank is full.

At t=0 the tank is empty

(c)

Time       volume

 0               50 gal

 5                37.5 gal

 10              25 gal

 15             12.5 gal

20                0 gal

(d)

Net change of volume = 50 gal

Step-by-step explanation:

Given that the capacity of the tank is 50 gal.

Torricelli's Law gives the volume of water remaining in the tank after t minutes as

[tex]V(t)=50(1-\frac{t}{20})^2[/tex]

(a)

To find V(0), we put t = 0 in the above equation

[tex]V(0)=50(1-\frac{0}{20})^2[/tex]

        [tex]=50(1-0)^2[/tex]

        = 50 gal

To find V(20), we put t =2 0 in the above equation

[tex]V(20)=50(1-\frac{20}{20})^2[/tex]

        [tex]=50(1-1)^2[/tex]

        = 0 gal

(b)

At t= 0 the tank is full.

At t=0 the tank is empty.

(c)

Time                                          V(t)

  0                                  [tex]50(1-\frac{0}{20})^2=50 \ gal[/tex]

  5                                  [tex]50(1-\frac{5}{20})^2=37.5 \ gal[/tex]

 10                                  [tex]50(1-\frac{10}{20})^2=25 \ gal[/tex]

 15                                 [tex]50(1-\frac{15}{20})^2=12.5 \ gal[/tex]

 20                                [tex]50(1-\frac{20}{20})^2=0[/tex]

(d)

Net change of volume = V(0) -V(20)

                                     =(50-0) gal

                                    = 50 gal

The volume V(t) of water remaining in the tank after t minutes is given by V(t) = 50(1−t/20). V(0) represents the initial volume of water in the tank, which is 50 gallons. V(20) represents the volume of water remaining in the tank after 20 minutes, which is 0 gallons.

(a) To find V(0), substitute t = 0 into the equation V(t) = 50(1−t/20).

V(0) = 50(1−0/20) = 50(1−0) = 50(1) = 50

Similarly, to find V(20), substitute t = 20 into the equation V(t) = 50(1−t/20).

V(20) = 50(1−20/20) = 50(1−1) = 50(0) = 0

(b) V(0) represents the initial volume of water in the tank, which is 50 gallons. V(20) represents the volume of water remaining in the tank after 20 minutes, which is 0 gallons.

(c) Creating a table of values of V(t) for t = 0, 5, 10, 15, 20:

t | V(t)

--------------------

0 | 50

5 | 37.5

10 | 25

15 | 12.5

20 | 0

(d) The net change in volume V as t changes from 0 min to 20 min is V(20) - V(0).

V(20) - V(0) = 0 - 50 = -50 gallons

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Answer: [tex]m\angle A=116\°[/tex]

Step-by-step explanation:

The missing figure is attached.

For this exercise it is important to remember that, by definition, the opposite interior angles of an inscribed quadrilateral are supplementary, which means that their sum is 180 degrees.

Based on this, you can identify that the angle D and the angle B are opposite and, therefore, supplementary.

Knowing that, you can write the following equation:

[tex]x+28\°=180\°[/tex]

Now you must solve for "x" in order to find its value. This is:

[tex]x=180\°-28\°\\\\x=152\°[/tex]

Then:

[tex]m\angle D=152\°[/tex]

You know that:

[tex]m\angle A=(x-36)\°[/tex]

Therefore, since you know the value of "x", you can substitute it into   [tex]m\angle A=(x-36)\°[/tex] and then you must evaluate, in order to find the measure of the angle A. This is:

 [tex]m\angle A=152\°-36\°\\\\m\angle A=116\°[/tex]

Answer: P = Po ( 1 + 0.075)

Step-by-step explanation: let Po = initial population

P = final population.

The increase in population is by 7.5%, which implies that if the initial population Increases by 7.5%, we would have a new (current) population.

Final population = initial population + increament of initial population.

Where increment of initial population = 7.5% of Po = 0.075 Po

P = Po + 0.075Po

P = Po ( 1 + 0.075)

Answer:

D)191 feet

Step-by-step explanation:

Let the height of the light house be |AB| and the Boat be at point C as shown in the diagram.

The angle of depression of the boat from the top A of the lighthouse is given as 25 degrees

Angle BCA = 25 degrees (Alternate Angles are Equal)

We want to determine the distance of the boat C from the base of the lighthouse B i.e. |BC|

[tex]Tan\alpha =\frac{opposite}{adjacent}[/tex]

Tan 25=[tex]\frac{89}{|BC|}[/tex]

Cross multiply

|BC| X tan 25 =89

|BC| = [tex]\frac{89}{tan 25}[/tex]=190.86 feet

The distance of the boat C from the base of the lighthouse B is 191 feet (to the nearest feet).

Step-by-step explanation:

Below is an attachment containing the solution.

Paulina and Aliya's equations, 4x+2y=6 and 12x+6y=18, are multiples of each other. This means they represent the same line and indicate an infinite number of solutions rather than a single intersection point typically sought after in a system of distinct linear equations.

Paulina and Aliya have created linear equations to solve a mathematical problem. Paulina has the equation 4x+2y=6 and Aliya has 12x+6y=18. At a glance, these equations may look different, but upon closer inspection, Aliya's equation is actually just Paulina's equation multiplied by 3. This realization is pertinent because it suggests both equations represent the same line. Therefore, these two equations should have the same solution set.

To analytically solve simultaneous equations, one could use methods such as substitution, elimination, or matrix and determinant-based approaches. Using elimination or substitution, we aim to isolate one variable and solve for it. For example, because Aliya's equation is a multiple of Paulina's, if they were meant to be a system of separate lines, one way to solve them would be to simplify Aliya's equation by dividing by 3, revealing it to be identical to Paulina's, which indicates that this system has an infinite number of solutions (all points on the line represented by the equation).

If a system has two distinct equations, elimination involves adding or subtracting equations from one another to eliminate one of the variables, and substitution involves solving for one variable in terms of the other and then substituting this expression into the other equation. When equations are actually multiples of each other, this indicates either an infinite number of solutions or no solutions dependant if the equations are consistent or inconsistent respectively.

Answer:

A

Step-by-step explanation:

8(2) = 16

17 (2) = 34

34^2 = 16^2 + x^2

1156 = 256 + x^2

1156- 256 = x^2

900 = x^2

square root of 900 = x

x = 30

15(2) = 30

Answer:

A 15a

Step-by-step explanation:

This is a right triangle so we can use the Pythagorean theorem

a^2 +b^2 = c^2  where a and b are the legs and c is the hypotenuse

Letting the unknown side be x

(8a)^2 + x^2 = (17a)^2

64a^2 + x^2= 289a^2

Subtracting 64a^2 from each side

64a^2 -64a^2 + x^2= 289a^2-64a^2

x^2 =225a^2

Taking the square root of each side

sqrt(x^2) =sqrt(225a^2)

x = 15a

[tex]\boldsymbol{\mathbf{Answer}}[/tex]

[tex]\boldsymbol{\mathbf{Machine \, A \,will\, take \,6 \,hours\, to \,produce\, 1 \,widget \,on\, its\, own.}}[/tex]

[tex]\boldsymbol{\mathbf{Step-by-step \,explanation:}}[/tex]

Let,

performance rate of machine A is x widget per hour.

performance rate of machine A is y widget per hour.

As given, Machine A and Machine B can produce 1 widget in 3 hours working together.

I.e mathemetically,

[tex]\boldsymbol{x + y=\frac{1}{3}......(1)}[/tex]

lly for second statement, Machine A’s speed were doubled, the two machines could produce 1 widget in 2 hours working together.

i.e mathematically,

[tex]\boldsymbol{2x + y=\frac{1}{2}......(2)}[/tex]

Substact equation (1) in (2)

  [tex]x + y=\frac{1}{3}[/tex]

[tex]-2x + y=\frac{1}{2}[/tex]

Resultant equation will be,

[tex]-x=\frac{-1}{6}[/tex]

[tex]\boldsymbol{x = \frac{1}{6}}[/tex]

Performance rate of machine A is \frac{1}{6} widget per hour.

what is time Machine A will take to produce 1 widget on its own.

i.e = [tex]\frac{1}{\frac{1}{6}}[/tex]

[tex]\boldsymbol\mathbf{{=\, 6 \,hours.}}[/tex]

The number of pennies and nickels that has a worth of $0.45 is 15 and 6 respectively

Given:

total worth = $0.45

Total coins = 21

let

number of pennies = x

number of nickels = y

x + y = 21 (1)

0.01x + 0.05y = 0.45 (2)

multiply (1) by 0.01

0.01x + 0.01y = 0.21 (3)

0.01x + 0.05y = 0.45 (2)

subtract (2) from (1)

0.05y - 0.01y = 0.45 - 0.21

0.04y = 0.24

y = 0.24 / 0.04

y = 6

substitute y = 6 into (1)

x + y = 21 (1)

x + 6 = 21

x = 21 - 6

x = 15

Therefore, the number of pennies and nickels that has a worth of $0.45 is 15 and 6 respectively.

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Answer:   [tex]\bold{(a)\quad \dfrac{32}{3}\qquad (b)\quad \dfrac{32}{3}}[/tex]

Step-by-step explanation:

(a) First, find the x-coordinates where the two equations cross

                            y = -1    and   y = 3 - x²

  -1 = 3 - x²

 -4 =     -x²

  4 =       x²

± 2 =       x       → These are the upper and lower limits of your integral

Then subtract the two equations and integrate with upper bound of x = 2 and lower bound of x = -2

[tex]\int_{-2}^{+2}[(3-x^2)-(-1)]dx\\\\\\=\int_{-2}^2(4-x^2)dx\\\\\\=4x-\dfrac{x^3}{3}\bigg|_{-2}^{+2}\\\\\\=\bigg(8-\dfrac{8}{3}\bigg)-\bigg(-8+\dfrac{8}{3}\bigg)\\\\\\=\large\boxed{\dfrac{32}{3}}[/tex]

(b) We know the upper and lower bounds of the y-axis as y = 3 and y = -1

Next, find the equation that we need to integrate by solving for x.

      y = 3 - x²

x² + y = 3

x²       = 3 - y

x         [tex]=\pm\sqrt{3-y}\\[/tex]

[tex]\rightarrow \qquad x=\sqrt{3-y}\quad and \quad x=-\sqrt{3-y}[/tex]

Now, subtract the two equations and integrate with upper bound of y = 3 and lower bound of y = -1

[tex]\int_{-1}^{+3}[(\sqrt{3-y})-(-\sqrt{3-y})]dy\\\\\\=\int_{-1}^{+3}(2\sqrt{3-y})dy\\\\\\=\dfrac{-4\sqrt{(3-y)^3}}{3}\bigg|_{-1}^{+3}\\\\\\=\bigg(0\bigg)-\bigg(-\dfrac{32}{3}\bigg)\\\\\\=\large\boxed{\dfrac{32}{3}}[/tex]

Answer:

Therefore the wire should be anchored at 10 ft away from pole which is 10 ft long.

Step-by-step explanation:

Given that , The distance between two poles is 30 ft.

The length of 1st pole is = 20 ft

The length of second pole is = 10 ft.

Let the wire anchored to the ground at a distance x ft from the second pole.

Then, the distance of anchored from the first pole is = (30-x)

The total length of the wire is L = m+n

We know the pythagorean theorem,

Height²+base² = hypotenuse²

To find the value of m and n we use  pythagorean theorem

From the left side triangle in the picture we get,

10²+x²= m²

⇒m²=100+x²

[tex]\Rightarrow m= \sqrt {100+x^2[/tex]

and right side  triangle in the picture we get,

20²+(30-x)² = n²

⇒n²= x²-60x+1300

[tex]\Rightarrow n= \sqrt {x^2 -60x+1300}[/tex]

Then ,

[tex]L= \sqrt{(100+x^2)}+\sqrt{(x^2-60x+1300) }[/tex]

Differentiating with respect to x

[tex]L'= \frac {2x}{2\sqrt{100+x^2}}+ \frac{2x-60}{2\sqrt {x^2-60x+1300}}[/tex]

For minimize, L' =0

[tex]\frac {2x}{2\sqrt{100+x^2}}+ \frac{2x-60}{2\sqrt {x^2-60x+1300}}=0[/tex]

[tex]\Rightarrow \frac {x}{\sqrt{100+x^2}}=- \frac{x-30}{\sqrt {x^2-60x+1300}}[/tex]

Squaring both sides

[tex]\Rightarrow( \frac {x}{\sqrt{100+x^2}})^2=(- \frac{x-30}{\sqrt {x^2-60x+1300}})^2[/tex]

[tex]\Rightarrow x^2(x^2-60x+1300)= (x^2-60x+900)(100+x^2)[/tex]

[tex]\Rightarrow x^4 -60x^3+1300x^2= 100x^2-6000x+90000+x^4-60x^3+900x^2[/tex]

[tex]\Rightarrow 300x^2+6000x-90000=0[/tex]

[tex]\Rightarrow x^2+20x-300=0[/tex]

[tex]\Rightarrow x=10,-30[/tex]

Therefore x = 10. [x=-30 negligible, since distance can not negative]

Therefore the wire should be anchored at 10 ft away from pole which is 10 ft long.

The problem can be solved geometrically through the principles of trigonometry. By setting up two right triangles formed by the telephone poles and the anchoring point, we can create two equations by Pythagorean Theorem. By taking the derivative of the total wire length and setting it to zero, we can find the optimal value for 'x' (location of the anchoring point) which results in the minimal amount of wire used.

To solve for the minimal amount of wire needed, we can use the principles of mathematics. More specifically, we will use the concept of trigonometry and geometry to create two right triangles. The taller pole (20ft), the shorter pole (10ft) and the point on the ground where the wire is anchored form the two right triangles, one with 20ft height and another with 10ft height.

Let's denote the length of wire between the taller pole and ground as 'a', between the shorter pole and the ground as 'b', and the distance between the point on the ground where the wire is anchored and the base of the first pole as 'x'. We have:

The total length of wire used (which we want to minimize) is a + b.

To find the minimal length, we can take the derivative of 'a+b' with respect to 'x' and set the derivative equation to 0 then solve for 'x'. This will give you where to place the anchor on the ground (minimal amount of wire used) between the two poles. You may find out an optimal 'x' value that is less than 30ft, ensuring that the anchoring point is between the two poles.

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Answer: U' = (0, 1)

Step-by-step explanation:

U = (3, -5)

rotate 90° counterclockwise means (x, y) = (-y, x)

new U = (5, 3)

down 2 units means subtract 2 from the y-coordinate

newer U = (5, 1)

left 5 units means subtract 5 from the x-coordinate

U' = (0, 1)

Final answer:

The antique purchased by Juan increases in value by 10% each year. The value of the antique after 2 years can be found by calculating the expression $200a, where a is a constant. The value of [tex]\( a \) is \( 1.21 \).[/tex]

Explanation:

To find the value of a, we need to represent the annual increase of 10% in terms of multiplication.

After the first year, the value of the antique increases by [tex]\( 10\% \) of its previous value, which is \( 0.10 \times 200 \) dollars.[/tex]

After the second year, the value of the antique increases by [tex]\( 10\% \) of its value at the end of the first year, which is \( 0.10 \times (200 + 0.10 \times 200) \) dollars.[/tex]

Generally, after \( n \) years, the value of the antique will be [tex]\( 200 \times (1 + 0.10)^n \) dollars.[/tex]

The expression given for the value of the antique 2  years after purchase is 200a , where a is a constant. This represents the value of the antique after 2  years.

Equating the expression to the value of the antique after 2 years, we have:

[tex]\[ 200a = 200 \times (1 + 0.10)^2 \][/tex]

Now, let's solve for \( a \):

[tex]\[ 200a = 200 \times (1.10)^2 \][/tex]

200a = 200 \times 1.21

200a = 242

Dividing both sides by 200:

[tex]\[ a = \frac{242}{200} \][/tex]

[tex]\[ a = 1.21 \][/tex]

Therefore, the value of [tex]\( a \) is \( 1.21 \).[/tex]

Answer:

The assumption will depend on the argument that C. Any decrease in per capita sales of cigarettes in Coponia will result mainly from an increase in the number of people who quit smoking entirely.

Step-by-step explanation:

Per capita income or average income measures the average income earned per person in a given area in a specified year. It is calculated by dividing the area's total income by its total population. Per capita income is national income divided by population size.

Tax is a compulsory contribution to state revenue, levied by the government on workers' income and business profits, or added to the cost of some goods, services, and transactions.

Answer:

Explanation:

The "Shortest Route Algorigtm" aims to determine the most efficient or short route, when a several alternative pahtways can connect or be used to implement a solution.

A graph is drawn with the different nodes and paths that connect them. The distance between every pair of consecutive nodes is written.

The picture shows that for the step #1, there are, in principle, three routes: AB, AC, and AD.

AB must be discarded because it is not viable (a negative distance is not possible).

AC is more efficient than AD because the distance of AC is 3 and the distance of AD is 8. Thus AC is selected and circled.

To continue from AC, the possible routes are shown in step #2. They are ACB; 3 and ACE; 6.

ACB i s shorter, thus ACB is circled.

In step #3, the possible routes are ACBE; 8 and ACBD; 7. Thus, route ACBD is shorter, and it shall be circled.

The conclusion of the algorithm is that the route ACBD is the shoretes (most efficient).

The route to circle next is route ACBD; 7

From the question, we understand that she wants to determine the shortest route.

This means that, she has to circle the node with the smallest value in each step.

From the diagram, the smallest node in step 3 is ACBD; 7

Hence, the route to circle next is route ACBD; 7

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Answer:

The given data is not normal.

Step-by-step explanation:

We are given the following data:

30, 59, 69, 50, 58, 71, 55, 43, 3,  66, 52, 56, 62, 36, 13, 29, 17, 31

Condition for normality:

Mean = Mode = Median

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{800}{18} = 44.44[/tex]

Mode is the most frequent observation of the data.

Since all the value appeared once, there is no mode.

[tex]Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}[/tex]

Sorted data: 3, 13, 17, 29, 30, 31, 36, 43, 50, 52, 55, 56, 58, 59, 62, 66, 69, 71

Median =

[tex]=\dfrac{9^{th}+10^{th}}{2} = \dfrac{50+52}{2}=51[/tex]

Since the mean, mode and median of data are not equal, the data is not normal.

Answer:

0.900

Step-by-step explanation:

The easiest way to solve this problem is by putting it into a calculator.

When put into a calculator, the answer comes out to be 0.9004304526, which can be rounded to 0.900, or just 0.9.

Good morning ☕️

Answer:

0.900

Step-by-step explanation:

using a calculator you’ll find:

sin⁻¹(-0.435) = -25.785293878311

now

cos(sin⁻¹(-0.435)) = cos(-25.785293878311)

                           = 0.900430452617

If we round 0.900430452617 to nearest thousandth we get: 0.900

:)

From the given info (and the linked question) we find

[tex]\cos\alpha=-\dfrac5{13}[/tex]

[tex]\sin\alpha=\dfrac{12}{13}[/tex]

[tex]\sin\beta=-\dfrac45[/tex]

Then using the angle-sum identity for cosine, we have

[tex]\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta[/tex]

[tex]\cos(\alpha-\beta)=\left(-\dfrac5{13}\right)\dfrac35+\dfrac{12}{13}\left(-\dfrac45\right)=-\dfrac{63}{65}[/tex]

Final answer:

To find the exact value of cos(α-β), we use the cosine sum and difference identity and the respective sine and cosine values calculated from the given tangent and cosine values for angles α and β. Using this approach, we find that cos(α-β) equals 63/65.

Explanation:

The exact value of cos(α-β) can be found by using the sum and difference identities for cosine. Since tanα = -12/5, in quadrant II, we can find the corresponding sine and cosine values for α using the Pythagorean identity sin²α + cos²α = 1. For cosβ = 3/5, in quadrant IV, we do a similar procedure to find the sine of β. With both sine and cosine for α and β, we use the identity cos(A-B) = cosA cosB + sinA sinB to find cos(α-β).

To find the sine and cosine for α, given that tanα = -12/5, we know that the opposite side is -12, and the adjacent side is 5, so the hypotenuse using the Pythagorean theorem is √(12² + 5²) = √(144+25) = √169 = 13. Thus sinα = -12/13 (negative because α lies in the second quadrant where sine is negative) and cosα = 5/13 (positive because cosine in the second quadrant is positive).

For β, we already have cosβ = 3/5. The sine can be found using the Pythagorean identity 1 - cos²β = sin²β, which gives sinβ = -√(1 - (3/5)�) = -√(1 - 9/25) = -√(16/25) = -4/5 (negative because β is in the fourth quadrant where sine is negative).

Now, we can find the exact value of cos(α-β) by plugging in the values:

cos(α-β) = cosα cosβ + sinα sinβ = (5/13)*(3/5) + (-12/13)*(-4/5)
= 15/65 + 48/65 = 63/65.

Therefore, the exact value of cos(α-β) is 63/65.