A sight-seeing boat travels at an average speed of 21 miles per hour in the calm water of a large lake. The same boat is also used for sight-seeing in a nearby river. In the river, the boat travels 2.6 miles downstream (with the current) in the same amount of time it takes to travel 2 miles upstream (against the current). Find the current of the river.

Part A:

This data appears to be modeling a geometric sequence because the time to complete each station is increasing by a constant factor. For example, the time to complete station 2 is 4 minutes, which is double the time it took to complete station 1. Similarly, the time to complete station 3 is 8 minutes, which is double the time it took to complete station 2, and so on.

Part B:

To find the time Aurora will take to complete station 5 using a recursive formula, we can use the formula:

a_n = a_1 * r^(n-1)

where a_n is the time it takes to complete station n, a_1 is the time it takes to complete station 1, and r is the common ratio (the factor by which the time increases from one station to the next).

We are given that a_1 = 2 and a_2 = 4, so we can solve for r:

r = a_2 / a_1

= 4 / 2

= 2

Then we can use this value of r to find the time it takes to complete station 5:

a_5 = a_1 * r^(5-1)

= 2 * 2^4

= 2 * 16

= 32

Therefore, Aurora will take 32 minutes to complete station 5.

Part C:

To find the time Aurora will take to complete station 9 using an explicit formula, we can use the formula:

a_n = a_1 * r^(n-1)

where a_n is the time it takes to complete station n, a_1 is the time it takes to complete station 1, and r is the common ratio (the factor by which the time increases from one station to the next).

We are given that a_1 = 2 and a_2 = 4, so we can solve for r:

r = a_2 / a_1

= 4 / 2

= 2

Then we can use this value of r to find the time it takes to complete station 9:

a_9 = a_1 * r^(9-1)

= 2 * 2^8

= 2 * 256

= 512

Therefore, Aurora will take 512 minutes to complete station 9.

say no more

Answer:

the equation 10 = x - y

Step-by-step explanation:

Let x represent the initial value of the investment, and let y represent the amount of money that each person receives after the investment is withdrawn.

We know that the cost of withdrawing the investment is $10, so we can write the equation 10 = x - y. We also know that each person receives $40, so we can write the equation y = 40.

We can now solve for x by substituting the value of y into the first equation. Since y = 40, we can substitute 40 for y in the equation 10 = x - y to get 10 = x - 40. Solving this equation for x, we find that x = 50.

Therefore, the initial value of the investment was $50.

Answer:

30

Step-by-step explanation:

40% of what number is 12?

.4n = 12  Divide both sides by .4

n = 30

Answer:

30

Based on the given conditions, formulate: 12/40%

Multiply both the numerator and denominator with the same integer: 120/40

Cross out the common factor:30

Answer: 30

Step-by-step explanation:

y = mx + b

m = 3

b = 2

y = 3x + 2

______________________

y = mx + b

m = 1/2

b = -1

y = 1/2x + (-1)

y = 1/2x -1

With the Application of Algebraic expression first minute call charge is $1.126 and next every minute will be charge at $0.14

what is Algebraic expression?

Using the operations +, -,, or, a group of numbers or variables can be combined to form an expression. Expressions in algebra that include variables, numbers, and mathematical operators differ from expressions in arithmetic that simply contain numbers and mathematical operators.

solution:

Let first min charge =x

And charge for each additional minute = y

Now we have two equations

x+11y=2.35……(1)

x+17y=3.65……..(2)

Sub. (1) from (2)

6y = 1.3

y= 0.316

Put value in equation (1)

x+11×0.316=2.35

x=2.35- 3.476

X= 1.126

Therefore, first minute call charge is $1.126 and next every minute will be charge at $0.14

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The correct match for each linear system with one of the phase plane direction fields will be:

1:B

2:C

3:D

4:A

What is plane?

In geometry, a plane is a surface made up of all the straight lines connecting any two locations on it. It is, in other words, a level or flat surface. A plane is uniquely defined in a Euclidean space of any number of dimensions by one of the following: three non-collinear points are used. Other names for it include a two-dimensional surface. A plane has an unlimited width, an endless length, zero thickness, and no curvature. The flat surfaces of a cube or cuboid, as well as the flat surface of paper, are all true instances of geometric planes, despite the fact that it is difficult to envision a plane in real life.

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-3+9. -6

------= ---

-2+3. -1

the answer is 6

Answer:

66

Step-by-step explanation:

y = 58 e^(0.027 * 5)

y = 58 e^(0.135)

y = 58 * 1.144537

y = 66.383133

y = 66

The correct answer to the task above about the statements which identifies and describes the student model that is most consistent with the data in the table is:

What is describes?

To describe something is to put into words its appearance, nature, attributes, etc. The word is frequently used to describe a scene or an event with vividness of personal perception. To narrate is to describe what happened in detail, usually by describing an event or series of events in the chronological sequence in which they occurred.

Student Model 1 shows that sharks and ray-finned fishes share some structural similarities and are the most closely related among the four groups.

The correct answer choice is option b.

What is meant by the classification of living organisms?

The classification of living organisms simply refers to the grouping of living things together on the basis of their similarities and differences.

However, based on the information given on the table in the image above, the sharks and ray-finned fishes share some structural similarities and are the most closely related among the four groups which is most consistent therein.

In conclusion, it can therefore be deduced from the explanation given above that the students model 1 gave a very good description of features which are consistent in the organisms.

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(a) The probability that more than three aircraft arrive within an hour is 0.2970.

(b) The probability that no interval contains more than three arrivals is 2.56.

(c) The length of an interval of time is 0.891 hours.

The time between arrivals of small aircraft at a country airport is exponentially distributed with a mean of one hour.

(a) We will find the probability that more than three aircraft arrive within an hour,

P(X > 3) = 1 - P(X ≤ 3)

             = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3))

             = 1 - [ ( [tex]e^{-4/3}[/tex] 1° / 0!) + ( [tex]e^{-4/3}[/tex] 1¹ / 1!) + ( [tex]e^{-4/3}[/tex] 1² / 2!) + [tex]e^{-4/3}[/tex] 1³/ 3!]

             = 1 - (0.7029)

P(X > 3) = 0.2970

(b) Now we calculate probability that no interval contains more than three arrivals if 30 separate one-hour intervals are chosen,

(1 - P(X > 3)³°) = (1 - 0.2970)³°

                      = 2.56

(c) Let the length of an interval of time is t, the calculation for t is given as;

P(X = 0) = 0.41

[tex]e^{-t}[/tex](t)° / 0! = 0.41

          [tex]e^{-t}[/tex] = 0.41

          - t = ln(0.41)

          - t = -0.891

            t = 0.891 hours

Therefore the length of an interval of time such that the probability that no arrivals occur during the interval is 0.41 is 0.891 hours.

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Andrea could use 28÷7 = 4 this division problem to check her work.

Check one-by-one:

A. 0÷4=7

The answer to 7 divided by 0 is 0. This is due to the fact that dividing a non-zero number by zero is mathematically impossible. See complete response below.

B. 7÷4 = 28

7 * 4 = 28 is the correct value where this value is 1.7

C. 14÷4 = 7

The value of the above is not equated because 3.5 ≠ 7

D. 21÷7 = 4

Where 21÷7  is 3. Hence this is also not a correct answer.

E. 28÷7=4

7 * 4 = 28, which is correct equation.

Hence, Andrea could use 28÷7 = 4 this division problem to check her work.

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Answer:

Below

Step-by-step explanation:

bench     +   ( bench + 57)     = 1007

2 bench = 950

bench = $ 475

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex][tex]\begin{cases} h=1\\ k=3 \end{cases}\implies y=a(x-1)^2 + 3\hspace{5em}\textit{we also know that} \begin{cases} x=2\\ y=5 \end{cases} \\\\\\ 5=a(2-1)^2 + 3\implies 2=a(1)^2\implies \cfrac{2}{(1)^2}\implies 2=a \\\\\\ ~\hfill {\Large \begin{array}{llll} y=2(x-1)^2 +3 \end{array}} ~\hfill[/tex]

The value of x is 3 units.

What is the mid-point segment of the triangle?

The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

We have,

In ΔBCD

QR = x - 2 units

BD = x + 7 units

A line segment that connects two midpoints of the sides of a triangle is called a midsegment.

Mid-point segment of the triangle:

QR = 1/2(BD)         .............(1)

x - 2 = 1/2(x + 7)

2(x - 2) = x + 7

2x - 4 = x + 7

2x - x = 7 - 4

x = 3

Hence,  the value of x is 3 units.

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The two equations that could be used to find the number of

treats each dog gets is B) 18 / 6 = 3 and 6 X 3 = 18 So, the option B is the correct answer

What is an equation?

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. Since we can balance this by deducting the right-side expression from both sides' expressions, this won't limit the generality.

A condition on a variable is what an equation in algebra is. It can only be satisfied if the variable has a specific value. That indicates that only the value of x = 9 may satisfy the equation 2x - 5 = 13.

There are several sorts of equations as well, including:

Linear equations

Quadratic equations

cube-based equations

Differential equations

Parametric equations

As Tolen has 18 dog treats and he has 6 dogs to feed so each dog will get 3 treats i.e. (18 / 6 = 3) or we can there are 6 dogs and Tolen has 18 dog  treats to finish so he will give 3 dog treats to each dog  i.e.

(6 X 3 = 18)

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She should divide both sides by -5 while she multiplied by -5 on other side and she also did not change the > symbol to a < symbol

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has different meanings to different people, it is prone to misunderstanding in public discourse. However, some distinctions are shared.

We are given

-5x - 3.5>6.5

Since, we have to solve for x

so, we will isolate x on anyone side

step-1:

Add both sides by 3.5

-5x - 3.5+3.5>6.5+3.5

-5x>10

step-2:

Divide both sides by -5

we know that whenever we divide both sides by negative sign , it's inequality gets revered

so, we get

-5x/5<-50/-5

we get

x<10

so,

She should divide both sides by -5 while she multiplied by -5 on other side and she also did not change the > symbol to a < symbol

The complete question is : Parul attempted to solve an inequality but made one or more errors. Her work and the graph she drew are shown below. What errors did Parul make? Check all that apply. She added 3.5 to both sides when she should have subtracted. She should have divided both sides by as her first step. She divided one side by -5 while multiplying the other side by -5. She did not change the > symbol to a < symbol. She used a closed circle instead of an open circle on the number line.

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a) The hypothesis are given as follows:

b) The test statistic is of: z = 0.94.

c) The p-value is of: 0.1736.

At the null hypothesis, it is tested if there is not enough evidence that p1 is greater than p2, that is, if the subtraction is of zero, hence:

[tex]H_0: p_d = 0[/tex].

At the alternative hypothesis, it is tested if there is enough evidence that p1 is greater than p2, that is, if the subtraction is greather than zero, hence:

[tex]H_1: p_d > 0[/tex].

For each sample, the mean and the standard error are given as follows:

Hence, for the distribution of differences, the mean and the standard error are given as follows:

The test statistic is given by the division of the estimate of the proportion of differences by the standard error, hence:

z = 0.0395/0.0421 = 0.94.

We have a right-tailed test, as we are testing if the mean is greater than a value, with z = 0.94. Hence, looking at the z-table, the p-value is of:

0.1736.

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Answer:

56.7C

Step-by-step explanation:

The highest temperature on the was 56.7C and it is recorded in United States on 10 July 1913

Answer:

  z ∈ (-∞, -3]

Step-by-step explanation:

You want the solution to −2(2z−3)≥2z+24.

Simplify the inequality:

  -4z +6 ≥ 2z +24

  -18 ≥ 6z . . . . . . . . . add 4z -24

  -3 ≥ z . . . . . . . . divide by 6

The solution is z ∈ (-∞, -3].

The distance between any coordinate (x,y) and the origin is given by the equation presented as follows:

D = square root of (x² + y²).

The angle between these coordinates and the positive x-axis is given as follows:

Angle = arctan(y/x).

The distance between two points on a coordinate line is equivalent to the hypotenuse of a right triangle.

The sides of the triangle are represented by the differences of the x-coordinates and the y-coordinates of each point.

For the origin, the coordinates are (0,0), hence the distance of any point from the origin is given by the equation presented as follows:

D = square root of (x² + y²).

For the angle, we have that:

Hence the tangent is applied, as follows:

tan(Angle) = y/x

Angle = arctan(y/x).

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slope(m) of the perpendicular line is 1/3.

Slope of a line in mathematics is defined as its steepness. It is calculated as rise(difference of y- coordinates) over run(differences of x- coordinates) .

Two lines which intercept each other at an angle of 90 degree are known as perpendicular lines.

According to the given data and using the formula of perpendicular slope(m1*m2=-1);

Slope(m1) of original line =-3

Let the slope of perpendicular line be m2

m1*m2=-1

-3*m2=-1

m2=1/3

hence slope (m2) =1/3

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The graph of the inequality is attached.

What is closed circle in inequality?

Open circles are used for numbers that are less than or greater than (< or >). Closed circles are used for numbers that are less than or equal to and greater than or equal to (≤ or ≥).

Given inequality is x > 3.2.

The inequality sign of the given inequality is grater than.

The graph of the inequality will starts with open circle.

Since x is greater than 3.2. Therefore the given inequality will represent all real numbers that are greater than 3.2.

Thus the inequality will represent all number that lie on right of 3.2 on the number line.

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The value of ∠ DEG = 20° in the given triangle. The value of b in the given triangle is 22.6.

a) ∠ DEG = ? if ∠DFE = 70°

Here, ∠F = ∠D = 70°

∠G = 90°

Sum of triangle = 180°

∠D + ∠E + ∠G = 180°

70° + 90° + x = 180°

160° + x = 180°

x = 180° - 160°

x = 20°

b) if a = 8 , c =24 then b = ?

∠DGE is right angle. It follows Pythagoras theorem:

What is pythagoras theorem?

DG² + GE² = DF²

8² + X² = 24²

X² = 576 - 64

X² = 512

X = 22.6

Hence, the value of b in the given triangle is 22.6.

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Answer:

  A.  $510.75

  B.  $6,129.00

  C.  8.63%

Step-by-step explanation:

You want the monthly payments, total amount paid, and fraction going to interest for the payoff of a $5600 credit card balance at an annual rate of 17% interest.

The monthly payments can be found using the amortization formula:

  A = P(r/12)/(1 -(1 +r/12)^(-12)) . . . . . P is the principal amount, r is the rate

This formula gives the monthly payment for payoff in 1 year.

  A = 5600(0.17/12)/(1 -(1 +0.17/12)^-12) ≈ 510.75

The monthly payment is $510.75.

You will have made 12 monthly payments of $510.75, for a total of ...

  12 ×  $510.75 = $6,129.00

You will have paid $6,129.00.

The fraction of your total payoff that goes to interest is ...

  (6129 -5600)/6129 = 1 -(5600/6129) ≈ 0.0863 = 8.63%

About 8.63% of your total payment is interest.

__

Additional comment

Spreadsheets and calculator apps can be used to find these values. You need to be careful to specify that payments are made at the end of the month.

The amount to interest is slightly more than half the interest that would be due if the interest rate were used to calculate simple interest. Our answer of 8.63% is slightly higher than 17%/2 = 8.5%, so passes the reasonableness check.

The difference between the low temperature and the high temperature on Tuesday is -1.1°C.

From the information given, the temperature Monday evening was 16.4 c the temperature dropped an average of 1 1/4 degrees each hour for the next 14 hours until it reached its lowest temperature for the day on Tuesday.

Therefore, the temperature on Tuesday will be:

= 1 1/4(14)

= 17.5

The difference in the temperature will then be:

= 16.4°C - 17.5°C

= -1.1°C.

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Answer:

its the first option explanation is up top

The solution to the given integration problem is;

[tex]\frac{[(x^{2} + 1)x^{\frac{3}{2} } *(3x^2 - 2)]}{15} + C[/tex]

We want to integrate the function x³[√(x² + 1)dx]

This is expressed as;

∫x³[√(x² + 1)dx]

Preparing for substitution we have;

∫2x[x²√(x² + 1)/2dx]

Make u = x²

du/dx = 2x

dx = (1/2x) du

Thus, we now have;

¹/₂∫u√(u + 1)du

¹/₂∫(u^(3/2) - √u) du

Applying power rule and solving this gives us;

[tex]\frac{(x^2 + 1)x^{\frac{5}{2} } }{5} - \frac{(x^2 + 1)x^{\frac{3}{2} } }{3}[/tex]

= [(x² + 1)^(3/2) (3x² - 2)]/15 + C

Thus, that is the solution of solving the integration problem.

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