A cabin cruiser traveling with the current went 45 mi in 3 h. Traveling against the current, it took 5 h to go the same distance. Find the rate of the cabin cruiser in calm water and the rate of the current.

Answer:

It would take Sam 29 minutes and 30 seconds

Step-by-step explanation:

To Find : size of angle x

Solution:

Area of ΔABC = (1/2) * BC * AC

=> (1/2) * BC * AC = 42

=> (1/2) * 6 * AC = 42

=> AC = 14 cm

BD = BC + CD

=> 22 = 6 + CD

=> CD = 16 cm

Tan x = AC /CD

=> Tan x = 14/16

=> Tanx = 7/8

=> x = Tan⁻¹(7/8)

=> x = 41.186°

The size of the angle is - 41. 186°

    area of triangle ABC = 1/2 * BC * AC

    or, 1/2 *BC * AC = 42

     or, 1/2 * 6 * AC = 42

     or, 3 * AC = 42

divide both sides by 3,

        AC = 14 cm

     BD = BC + CD

or, 22 = 6 + CD

or, CD = 16 cm

   tan x = [tex]\frac{AC}{CD}[/tex]

or, tan x = [tex]\frac{14}{16}[/tex]

or, tan x = [tex]\frac{7}{8}[/tex]

or , x =  41. 186°

∴ The size of the angle is - 41. 186°.

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similar triangles have a ratio and in this case the ratio is 1:2 i hope you understand

Answer: y=-1/2x+4

Step-by-step explanation:

find the slope of the line given which would be-2/4 which simlifys down to 1/2 then add your b (y intercept) and that wold be 4.  

The common denominator of the fractions 2/3 and 1/6 will be 6.

The lowest common multiple is the smallest multiple which is common between any two numbers.

It means we can divide both numbers by that and that is the smallest number by which both dived.

As per the given fractions 2/3 and 1/6.

Multiply 2 in numerator and denominator in 2/3.

2/3 x 2/2 = 4/6

Now denominator is the same thus common denominator is 6.

Hence "6 will be the common denominator for the fractions 2/3 and 1/6".

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A  conditional probability p(b | a) is equal to its marginal probability p(b) if A and B are independent.

The likelihood that any two events will occur is equal to the sum of the probabilities of each event separately, less the probability that the two occurrences will meet. However, if two occurrences are incompatible with one another, then there is a zero probability of the two events intersecting, therefore the likelihood that either one or the other will occur is equal to the sum of the two individual probabilities.

To calculate conditional probability, use the following formula:

p( b | a ) = p( a ∩ b )/ p(a)

It is known that if two events A and B are independent, then p(a ∩ b) = p (a) . p(b)

So, p(b | a) = [p (a) . p(b)]/p(a) = p(b)

Thus, it is concluded that a conditional probability p(b | a) is equal to its marginal probability p(b) if A and B are independent.

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The domain and range for the following graph, is written below:

Domain (interval notation) : [-4,4)

Range (interval notation): [1,4)

Domain (inequality notation): -4 ≤ x < 4

Range (inequality notation): 1 ≤ x < 4

The collection of values that can be put into a function's domain are called its parameters. The x values for a function like f(x) are contained in this collection (x). The collection of values that a function can take on is known as its range. Following the putting of the x value, the function outputs this sequence of values.

Utilizing graphs is a useful tool for determining the scope and range of functions. A graph's domain is the entire set of input values shown on the x-axis since the term "domain" refers to the set of potential input values. The various output values are displayed on the y-axis and make up the range.

Domain (interval notation) : [-4,4)

Range (interval notation): [1,4)

Domain (inequality notation): -4 ≤ x < 4

Range (inequality notation): 1 ≤ x < 4

As we know,

Domain is the x-values of a function

Range is the y values of a function

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The ordered pair that is a solution to the given equation, y = | -6x + 2 |, is (1, 4)

From the question, we are to determine the ordered pair that is a solution of the given equation

The given equation is

y = | -6x + 2 |

To determine the ordered pair that is a solution to the equation, we will pick a value for x and determine the value of y for the value

y = | -6x + 2 |

Put x = 1

y = | -6(1) + 2 |

y = | -6 + 2 |

y = | -4 |

y = 4

Hence, the ordered pair is (1, 4)

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The answer as a mixed number in simplest form will be 1 3/4.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The expression is,

⇒ 1/4 - (- 1 1/2)

Now,

Since, The expression is,

⇒ 1/4 - (- 1 1/2)

Hence, Solve the expression as;

⇒ 1/4 - (- 1 1/2) = 1/4 + 3/2

                      = 1/4 + 6/4

                      = 7/4

                      = 1 3/4

Thus, The answer as a mixed number in simplest form will be 1 3/4.

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if f(x) +[tex]x^{2}[/tex]  [tex][ f(x) ]^{5}[/tex]  = 34 and f(1) = 2, then f '(1) = - [tex]\frac{64}{81}[/tex]

f ′(x )'s indicates that it is derived from f (x). The second notation is dydx. The instantaneous rate at which y changes in relation to x is shown by this notation.

f(x) + [tex]x^{2}[/tex]  [tex][ f(x) ]^{5}[/tex]  =  34

differentiate with respect to x :

f' (x) + [tex]x^{2}[/tex] . 5 [tex][ f(x) ]^{4}[/tex] f'(x) +  [tex][ f(x) ]^{5}[/tex]  2x = 0

putting x = 1

f' (1) + [tex]1^{2}[/tex] . 5  [tex]f(1)^{4}[/tex] f'(1) + [tex]f(1)^{5}[/tex] 2(1) = 0

f' (1) + 1.5 [tex](2)^{4}[/tex] f'(1) + [tex](2)^{5}[/tex] . 2 = 0

f' (1) + 80 f' (1) = - 64

81 f' (1) = - 64

f' (1) = - [tex]\frac{64}{81}[/tex]                    

thus , the f ' (1) is found.

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equation will be the number of shirts ordered in each size. division equation with that model the theory 45 ÷ 5 = 9

The Harbor Lighthouse gift shop ordered a shipment of 45 shirts with a special whale print. This means that we need to divide 45 by 5, in order to find out how many shirts were ordered in each size. To do this, we can use a division equation.

In this equation, 45 represents the total number of shirts and 5 represents the number of sizes. The answer to this equation will be the number of shirts ordered in each size. When we divide 45 by 5, we get 9 as our answer. Therefore, the store ordered 9 shirts in each size.

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The vertical angles are congruent, then the two lines cut by a transversal are parallel is False.

Option B is the correct answer.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

Vertical angles are congruent.

Vertical angles are pairs of opposite angles made by intersecting lines.

Thus,

For vertical lines to be congruent, we do not need two parallel lines.

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Answer:

100n/m

Step-by-step explanation:

n = m% of x

n = mx/100

x = 100n/m

The point-slope form with a slope of 5/2 and a point of (4,-7) is 5x-2y=34.

What is line equation?

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10. Linear equations are classified into three types: point-slope, standard, and slope-intercept.

Here,

The slope of line perpendicular to the line y +6=-2/5(x-1)

m1=5/2

point=(4,-7)

y-y1=m(x-x1)

y+7=5/2(x-4)

2y+14=5x-20

5x-2y=34

The point-slope form for slope given as 5/2 and point as (4,-7) will be 5x-2y=34.

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Answer: x ≥ 8

Step-by-step explanation:

      We know that our inequality must be greater than or equal to $112 because she needs at least $112 to buy the new dress. This is the first part of our inequality.

      Next, we see that she already has $40 and will earn $9 an hour babysitting, if x is the number of hours. $9 an hour can become 9x, then we will add the $40 she already has for 9x + 40 as the second part of our inequality.

      This complete inequality is:

9x + 40 ≥ 112

      Now, we can solve by isolating the variable x with inverse operations.

9x + 40 ≥ 112

9x ≥ 72

x ≥ 8

      Matilda needs to babysit at least 8 hours to afford the new dress.

Answer:

The x-axis interval of 39 to 65 has the smallest rate of change.

Step-by-step explanation:

See the attached worksheet.  The interval of x that results in the least change in y can be visually seen by plotting the points and drawing a curve.  The curve begins to flatten as x increases.  So the smallest rate of change is between the last two points, x = 39 to 65.

This can also be calculated by finding the change in y per a change in x.  The table in the graph confirms the earlier observation.  Dx and Dy represent the "delta," or difference, D,  between the x (Dx) and y(Dy) values.  The rate of change is calculated as Dy/Dx, or the change in y divided by the change in x.  The results confirm that the 39 to 65 segment is the smallest, at 0.15.

Answer:

-38x - 14y

Step-by-step explanation:

2[x+2y - 24x - 12y + 4x + 3y]

2 [ -19x -7y]

- 38x - 14y

Answer:

the rationalized form of the denominator 1/(5^(1/2)-2) is (x+2)/((x-2)(x-1)(x+1)).

Step-by-step explanation:

Correctly me if im wrong. To rationalize the denominator of the fraction 1/(5^(1/2)-2), we can use the conjugate of the denominator. The conjugate of a+b is a-b, so the conjugate of 5^(1/2)-2 is 5^(1/2)+2. We can then multiply the numerator and denominator of the fraction by the conjugate to obtain:

1/(5^(1/2)-2) * (5^(1/2)+2)/(5^(1/2)+2)

= (1*(5^(1/2)+2)) / ((5^(1/2)-2)*(5^(1/2)+2))

= (5^(1/2)+2) / (5^2 - 2*5^(1/2) - 4)

Notice that we can further simplify this expression by substituting 5^(1/2) with x and expanding the denominator:

(5^(1/2)+2) / (5^2 - 2*5^(1/2) - 4)

= (x+2) / (x^2 - 2x - 4)

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

The denominator of this expression can be further simplified by factoring out x-2, which gives us:

(x+2) / (x-2)(x+2)

= (x+2) / (x-2)(x-2 + 4)

= (x+2) / (x-2)(x^2 - 2x + 4 - 4)

= (x+2) / (x-2)(x^2 - 2x)

= (x+2) / (x-2)((x-1)(x+1))
Finally, we can use the fact that x-1 and x+1 are factors of x^2-2x, which means that we can factor out x-1 and x+1 from the denominator to obtain the fully simplified expression:
(x+2) / (x-2)(x^2 - 2x)

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

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

Therefore, the rationalized form of the denominator 1/(5^(1/2)-2) is (x+2)/((x-2)(x-1)(x+1)).

The equation representing the total profit earned by Maon is Profit = 256 - 128.

Profit is calculated by the formula -

Profit = Cost price - Selling price

Cost price = 64×2

Performing multiplication to find the cost price

Cost price = $128

Selling price = 64×4

Performing multiplication to find the selling price

Selling price = $256

Keep the values in equation to find the profit

Profit = 256 - 128

Performing subtraction on Right Hand Side of the equation to find the profit

Profit = 128

Thus, the profit earned is $128.

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Answer:

11/50

Step-by-step explanation:

=5x2+1= 11/5

=1/10×11×5

=11/50

Answer: The y-intercept is 14

Step-by-step explanation:

The slope intercept is y=mx+b

since we already have the slope, we can write this as

y=-5x+b

substitute the points of (3,-1) into the equation and solve for b

-1=-5(3)+b

-1=-15+b

b=14

The y-intercept is 14

The y-intercept of the line is 14.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Slope = -5

The line passes through the point (3, -1).

The equation of the line is y = mx + c.

y = -5x + c

(3, -1) = (x, y)

-1 = -5 x 3 + c

-1 = -15 + c

-1 + 15 = c

c = 14

Thus,

The y-intercept is 14.

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The cylindrical coordinates of (−7, 7, 7) are (√98, -π/4, 7). cylindrical coordinate (−7, 7 3 , 1) is  (14, -π/3, 1).

We must switch from rectangular to cylindrical coordinates in the provided problem. (let r ≥ 0 and 0 ≤ θ ≤ 2π.)

A)(−7, 7, 7)

Given rectangular coordinates(x, y, z) =(−7, 7, 7)

The cylindrical coordinates are (r, θ, z)

As a result, we determine each value of r and θ  separately.

r = √x²+y²

r = √(-7)²+(7)²

r = √49+49

r = √98

θ = tan⁻¹ (y/x)

θ =tan⁻¹  (7/-7)

θ =tan⁻¹  (-1)

θ = -π/4

So cylindrical coordinate = (r, θ, z) = (√98, -π/4, 7)

B) (-7,7√3,1)

Given rectangular coordinates(x, y, z) = (-1,1,1)

The cylindrical coordinates are (r, θ, z)

As a result, we determine each value of r and θ  separately.

r = √x²+y²

r = √(-7)²(7√3)²

r = √49+147

r = √196

r = 14

θ = (y/x)

θ = (7√3/-7)

θ = (-√3)

θ = -π/3

So cylindrical coordinate = (r, θ, z) = (14, -π/3, 1)

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Answer:

Below

Step-by-step explanation:

1500 = 1000 e^.03t

1.5 = e^.03t

take LN of both sides

.405465 = .03 t        t =13.5 yrs

Ms. Jones washed most of the laundry and the remaining laundry need to be washed is 7/20.

Converting the fraction to decimal to easily compare the amount of laundry washed.

Laundry washed by Ms. Jones = 2/5

Performing division

Laundry washed by Ms. Jones = 0.4

Laundry washed by her son = 1/4

Performing division

Laundry washed by her son = 0.25

0.4 is greater than 0.25, hence, Ms. Jones washed more laundry.

They washed the laundry in fractions. So, the total laundry can be taken as 1.

Total laundry washed = 0.4 + 0.25

Total laundry washed = 0.65

Remaining laundry = 1 - 0.65

Performing subtraction

Remaining laundry = 0.35

Converting into fraction = 35/100

Remaining laundry in fraction = 7/20

Thus, Ms. Jones washed more laundry and 7/20 is remaining.

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The complete question is -

Ms. Jones washed 2/5 of her laundry. Her son washed 1/4 of it. How much of the laundry still needs to be washed?

The rate of interest for simple compounding if Louis is offered an interest rate of 6.35% for an investment with continuous compounding, is 0.0656 or 6.56%, so option D is correct.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

Louis is offered an interest rate of 6.35% for an investment with continuous compounding,

Here, P will be the same, the amount will be the same and the time period will be the same then,

The amount in simple compounding = The amount in continuous compounding

[tex]P(1 + r)^t = Pe^{rt}[/tex]

Here, r is the rate of interest for simple compounding,

[tex]1 + r = e^{0.0635}[/tex]   (All same quantities get canceled)

r = 1.0656 - 1

r = 0.06556

r = 0.0656

r = 6.56%

Thus, the rate of interest for simple compounding is 6.56%.

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The minimum value, Q1, Median, Q3 and maximum value of the data are 10,15,21.5, 23.5 and 27 respectively. The box-and-whisker plot of data is attached

Given: 21,27,22,22,25,14,16,10

Arrange the data in ascending or descending order:

10,14,16,21,22,22,25,27

The minimum value = 10. The maximum value = 27

Find the median. The median is the value in the middle. The median values are 21 and 22. Thus:

10,14,16,21,22,22,25,27

Median (Q2) = (21+22)/2 = 21.5

Consider the values to the left of the median with one of the median numbers included (since we have two numbers in the middle): 10,14,16,21

Median = (14+16)/2 = 15

Thus, Q1 = 15

Also, consider the values to the right of the median with one of the median numbers included: 22,22,25,27

Meadian = (22+25)/2 = 23.5

Thus, Q3 = 23.5

To create a box and whiskers plot use Minimum value, Maximum value, Q1, Median(Q2) and  Q3 (Check the attached image)

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Option D is correct the answer. The average rate of change over the interval 1 < x < 5 is greater than the average rate of change over the same interval for the function g(x) = 1. 8x2 is k(x) = 2x^2

The average rate of change:

Given a function y, the average rate of change S of y=f(x)  in an interval (xs,xf) will be given by the following equation:

[tex]S=\frac{f(xf)-f(xo)}{xf-xo}[/tex]

In this problem, we have that:

Interval (1,5), so xf=5,xo=1

Then

[tex]S=\frac{f(5)-f(1)}{4}[/tex]

All options are compared to g(x).

[tex]g(x)=1.8x^{2}[/tex]

g(5) = 1.8*(5)^2 = 45

g(1) = 1.8*(1)^2 = 1.8

[tex]S=\frac{45-1.8}{4} =10.8[/tex]

A.=f(x) = x^2

f(5) = 5^2 = 25

f(1) = 1^2 = 1

[tex]S=\frac{25-1}{4} =6.25[/tex]

Smaller than 10.8, so this is not the answer.

B.=g(x) = 1.2x^2

g(5) = 1.2*(5)^2 = 30

g(1) = 1.2*(1)^2 = 1.2

[tex]S=\frac{30-1.2}{4} =7.2[/tex]

Smaller than 10.8, so this is not the answer.

C.=h(x) = 1.5x^2

h(5) = 1.5*(5)^2 = 37.5

h(1) = 1.5*(1)^2 = 1.5

[tex]S=\frac{37.5-1.5}{4}= 9[/tex]

Smaller than 10.8, so this is not the answer.

D.=k(x) = 2x^2

k(5) = 2*(5)^2 = 50

k(1) = 2*(1)^2 = 2

[tex]S=\frac{50-2}{4} =12[/tex]

Greater than 10.8, this is the answer.

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