Use the diagram and the given angle measure to find the other three angle measures

The bearing of the helicopter from B to A is 75.96 degrees

Information from the question

A helicopter leaves A and flies 40 miles due east

the helicopter flies

10 miles due south

Work out the bearing of B from A = ?

The bearing from B to A is worked using SOH CAH TOA

The direction of movements describes a right angle triangle of

opposite = 40 miles

adjacent = 10 miles

The bearing is calculated using tan, TOA let the angle be x

tan x = Opposite / Adjacent

tan x = 40 / 10

tan x = 4

x = arc tan 4

x = 75.96 degrees

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The dimensions required to minimize the cost of fencing is 180ft and 360 ft.

According to question

The cost of fence on opposite side of river is $40.

The cost of fence on other sides of river is $10.

Total yield = 64800 sq. feet

Let the length of fence on the opposite side of fence be x and width of fence on the other side be y.

Area of fence = xy = 64800 sq feet

⇒ [tex]y = \frac{64800}{x}[/tex]

Let C be the cost of making fence.

For cost to be minimum, dC/dx should be equal to zero.

C = 40x + 10y * 2

⇒ C = [tex]40x + 10(\frac{64800}{x})*2[/tex]

⇒ [tex]\frac{dC}{dx} = 40 + 20 * 64800 * \frac{-1}{x^{2} } = 0[/tex]

⇒ [tex]40x^{2} = 20 * 64800[/tex]

⇒ [tex]x^{2} = 32400[/tex]

⇒ [tex]x = 180[/tex]

⇒ [tex]y = \frac{64800}{180} = 360[/tex]

So, the dimensions needed will be 180 ft and 360 ft.

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The relationship is not a proportional relationship between S and w.

Saving, S, after w weeks, is represented by the equation

S = 50+45w

If y is proportional to x, then

y ∝ x

y =kx

where k is the constant of proportionality.

Here, no constant term and (0,0) satisfies this equation.

The given equation is

S = 50+45w

Here, we have a constant term.

For S=0 and w=0,

0=50+45×0

0=50

Which is not true as 0 ≠ 50.

Since there is a constant term 50 and the equation is not valid for (0,0), therefore, the given relationship is not a proportional relationship.

I hope this answer helps.

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Answer:

OK, so we know that 50% of the 80 marbles is 40, but we are supposed to find 45% of it, so basically it is 36 marbles he has found, I hope this is right!

Love from Ella

The ratio of c and 10 is c:10.

According to the question,

We have the following information:

We have one variable and one number which are c and 10 respectively.

Now, we already know that ratio can be simply understood as division. So, to find the ratio of c and 10 we will divide c by 10. We also know that a variable can not be divided by a number.

(For example, x can not be divided by 20.)

So, we will replace the sign of division by that of the ratio.

c/10

c:10

Hence, the ratio of c and 10 is c:10.

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The percentage increase is 61.36%. If the airline charges an additional $50 baggage fee, the new percentage increase will be 45.68%.

A percentage increase denotes how much a percentage has risen over time. To get at this figure, discover the difference between the original and final values, then deduct it to get the actual sum of the decrease.

The idea of Percentage increase is simply the amount of increase from the original(initial) to the final figure expressed in terms of 100 parts of the original. E.g.  A 10% increase implies that if the original value is divided into 100 parts, the value has increased by an extra 10 parts. So, if the initial value rose by 16%, the value would rise by 16 for every 100 units, and so on.

The formula for calculating the percentage increase can be expressed as:

[tex]\%\ increase= \frac{new \ value - original \ value}{original \ value}\times 100[/tex]

[tex]\%\ increase= \frac{355- 220}{220}\times 100[/tex]

[tex]\%\ increase= \frac{135}{220}\times 100[/tex]

[tex]\mathbf{=61.36\%}[/tex]

[tex]New \ \%\ increase= \frac{new \ value - original \ value}{original \ value}\times 100[/tex]

[tex]New \ \%\ increase= \frac{405- 220}{405}\times 100[/tex]

[tex]New \ \%\ increase= \frac{185}{405}\times 100[/tex]

[tex]New \ \%\ increase=\mathbf{45.68\%}[/tex]

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The angle the road makes is 3.43°

What is an angle?

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Here, we have

A 6% downgrade means that for every 100 units of horizontal run.

The vertical height decreases by 6 units.

The grade has a downward angle of

tan⁻1(6/100) = 3.43°

Hence, the angle the road makes is 3.43°

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The distance between the two points (5,6) and (10,12) is [tex]\sqrt{61}[/tex]

What is the distance between two points formula?

The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a standard formula to calculate the distance between two points. This equation can calculate the separation between any two locations on an x-y plane.

Solution explained:

First, Write the distance formula:

[tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]

Now,

Substitute (5,6) and (10,12) into [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex] :

[tex]\sqrt{(10 - 5)^{2} + (12 - 6)^{2}}[/tex]      Calculate

[tex]\sqrt{(5)^{2} + (6)^{2}}[/tex]                      Calculate

[tex]\sqrt{25 + 36}[/tex]                            Calculate

Hence. the distance between points (5,6) and (10,12) is [tex]\sqrt{61}[/tex].

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Original equation (1/2) + (1/2x) = (x² -7x +10)/4x is equivalent to the proportion (x+1)/2x = (x² -7x +10)/4x.

As given in the question,

Given equation is :

Original equation (1/2) + (1/2x) = (x² -7x +10)/4x

Simplify the original equation to get the equivalent equation

Least common multiple is 2 and 2x is equal to 2x

Original equation (1/2) + (1/2x) = (x² -7x +10)/4x is Equivalent to the proportion is given by:

( x + 1) / 2x = (x² -7x +10)/4x

Therefore, original equation (1/2) + (1/2x) = (x² -7x +10)/4x is equivalent to the proportion (x+1)/2x = (x² -7x +10)/4x.

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Answer: 31, 33, 35

Step-by-step explanation:

Answer:

  124.2 miles

  ∠310.1°

Step-by-step explanation:

You want to know the bearing and distance to the airport from a plane that is 95 miles east and 80 miles south of it.

The Pythagorean theorem or the distance formula can be used to find the distance to the airport.

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((95 -0)² +(-80 -0)²) = √(9025 +6400) = √15425

  d ≈ 124.197 . . . . miles

The plane is about 124.2 miles from the airport.

The reference angle with respect to the +y axis can be found using the tangent relation.

  Tan = Opposite/Adjacent

  tan(α) = 95/80 = 19/16

  α = arctan(19/16) ≈ 49.9° . . . . . . CCW from +y axis

The bearing angle is measured clockwise from the +y axis (north), so is ...

  bearing = 360° -49.9° = 310.1°

The bearing to the airport is 310.1°.

__

Additional comment

Some navigators would refer to the bearing as N 49.9° W.

Less commonly, it might be referred to as W 40.1° N. Usually, N and S are the reference directions, with the modification being E or W from there. The less common usage might be chosen if an angle less than 45° is wanted.

The bearing is often reported to the nearest degree, without any degree symbol, as N50W.

The number of hours Serena and Roseline have to work to earn the same amount of money will be 9 hours.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Serena recently began working at the nearby salon. By and large, $58.50 in tips every day. Roseline recently began working at a bank. Since she doesn't get tips, she procures $16.35 60 minutes. The arrangement of conditions {y = 9.85x + 58.50 and y = 16.35x} can be utilized to address how much cash is procured, y, every day for working x hours.

The number of hours Serena and Roseline have to work to earn the same amount of money will be given as,

16.35x = 9.85x + 58.5

6.5x = 58.5

x = 9 hours

The number of hours Serena and Roseline have to work to earn the same amount of money will be 9 hours.

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Using the concepts of statistics, we got that  if the per capita death rate increased, then the exponential growth model would decrease the initial population size.

We know very well, the set up of a differential equation relating instantaneous population growth with respect to the time to the per capita population growth rate and the current population size at an arbitrary time is as follows:

dN / dt = rN

Now, we are told that the constant, r, is  per capita population growth rate. N is  current size of the population at some time. "r" is the "organisms added per reproductive period" divided by  total population at that time. For instance, if the 10 rabbits are born per month and the current population is 100 rabbits, then r value  = 0.1.

Hence, the exponential growth model  would decrease the initial population size  if the per capita death rate increased.

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The term for this kind of sample is cluster sampling

Given

that, At a major ten university, 200 of the 30,000 undergraduate students and 100 of the 5,000 graduate students are chosen to represent a sample of student opinion.

What is cluster sampling ?

Cluster sampling involves breaking up a population into smaller units called clusters. Then, they randomly select a sample from each of these clusters. Cluster sampling is a probability sampling technique that is frequently used to examine large populations, especially those that are widely geographically dispersed.

Researchers frequently refer to pre-existing groups like cities or schools when referring to clusters. With an SRS of 200 students and an SRS score of 100, clusters have been utilized in this instance. Cluster sampling is the name given to this type of sample as a result.

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The equations for the functions are f(x) = (-2/3)x - 8 and g(x) = (-2/3)x - 2

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

Using the two given points for f, we can find the slope:

m = (y2 - y1) / (x2 - x1)

m = (-6 - (-2)) / (-3 - (-9))

m = -4 / 6

m = -2/3

Let's use the point (-9, -2):

y - (-2) = (-2/3)(x - (-9))

y + 2 = (-2/3)(x + 9)

Multiplying both sides by 3 to get rid of the fraction:

3y + 6 = -2x - 18

3y = -2x - 24

y = (-2/3)x - 8

So the equation for f is:

f(x) = (-2/3)x - 8

To find the equation for g, we can use the fact that the y-intercept is 6 greater than the y-intercept of f. So if the y-intercept of f is b, then the y-intercept of g is b + 6.

f(x) = (-2/3)x - 8

0 = (-2/3)x - 8

2/3 x = -8

x = -12

The x-intercept of both f and g is -12.

Now we can use the y-intercept and x-intercept to write the equation for g. The slope of g is the same as the slope of f, which is -2/3.

y - (b + 6) = (-2/3)(x - (-12))

y - b - 6 = (-2/3)(x + 12)

Multiplying both sides by 3 to get rid of the fraction:

3y - 3b - 18 = -2x - 24

3y = -2x + 3b - 6

y = (-2/3)x + (3/3)b - 2

y = (-2/3)x + b - 2

So the equation for g is:

g(x) = (-2/3)x + b - 2

We know that the x-intercept of g is -12, so we can plug that in and solve for b:

0 = (-2/3)(-12) + b - 2

0 = 8 + b - 2

b = -6

So the y-intercept of g is -6 + 6 = 0.

Therefore, the equation for g is:

g(x) = (-2/3)x - 2

Hence , the equations for f and g are: f(x) = (-2/3)x - 8 and g(x) = (-2/3)x - 2

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Ana and Bonita were born nn year apart and its value of nn is 12.

Here we have to find nn which difference in the year in which Ana and Bonita were born.

Let x be the age of Ana and y be the age of Bonita.

It is given that last year Ana was 5 times as old as Bonita so from this statement we get the first equation:

x - 1 = 5(y -1)

x -1 = 5y - 5

5y -x = 4--------(1)

The second statement is Ana is square of Bonita's age. From this we get another equation:

x = y²-----------(2)

Putting equation 2 in equation 1 we get:

5y - y² = 4

y² - 5y +4 = 0

y² - 4y - y + 4 = 0

y(y-4) -1(y -4) = 0

(y - 4)(y -1) = 0

y = 4,1

As x = y²

x = 4² = 16 or x = 1² =1

We cannot take 1 as there is a difference in their age

So we get x = 16 and y =4

So the difference in their age = 16-4= 12

Therefore we get the value of nn as 12.

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Answer:

23%

Step-by-step explanation:

We can create two equations:

\[m = \frac{1}{5}(A - s)\]\[s  = \frac{1}{20}(A - m)\]

Substituting we get:

\[m = \frac{1}{5}(A - \frac{1}{20}(A - m))\]which yields:

\[m = \frac{19}{99}A\]

Now we can find s and we get:

\[s = \frac{4}{99}A\]

Since we want to find what fraction of $A$ did Roger pay for his movie ticket and soda, we add $m$ and $s$ to get:

\[\frac{19}{99}A + \frac{4}{99}A \implies \boxed{\text{(D)}\ 23\%}\]

The value of the equation y(t) at y(25) is 150

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Equations can be linear, quadratic or polynomials.

if y(t) = -14t + 500

The y(25)  means substitute t = 25 into the equation

y(25) = -14(25) + 500

y(25) = -350 + 500

y(25) = 150

In conclusion, the value of y(25) is 150

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It can take 3 years that a physics major to spend doing post-graduate research

Given that,

A physics professor is curious about the proportion of physics majors who will pursue post-graduate study during the coming years. He has the probability distribution shown below. x P(x) x*P (x) 1 0.35 2 0.20 3 0.15 4 5 0.10 6 0.05

To find P(X<=3)

P(X<=3)=P(X=0,1,2,3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)

            = 0.35+0.20+0.15

            = 0.7

P(X<=3)=0.7

Hence, A physics major may need to spend three years conducting post-graduate research. and the probability that a physics major will spend no more than three years conducting post-graduate research is 70% or 0.7

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Yes, he can mow the lawn in 2 hours.

We can define the work done as, a work done in a given period of time.

Given that, Theo mows a lawn. After working for 1 3/5 hours, he has mowed 7/9 of the lawn

In [tex]1\frac{3}{5}[/tex] hours he mows 7/9 part of lawn

Therefore, in 8/5 hours he is mowing 7/9 part of lawn

In 1 hour = 7/9*5/8 = 35/72

In 2 hours = 35/72*2 = 35/36 ≈ 1

Hence, Yes, he can mow the lawn in 2 hours.

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Answer:

x= 3.4

x+2= 5.4

x+3= 6.4

Step-by-step explanation:

Just figured it out :)

Solve in terms of x.

[tex]y=\frac{5}{x}[/tex]

Multiply by x on both sides to remove it from the denominator.

xy =5

Divide by y to get x by itself

[tex]x=\frac{5}{y}[/tex]

Answer:

x=5/y

Step-by-step explanation:

y=5/x

cross multiplying

yx=5

x=5/y

In the given equation, the value of n is (p - k - m).

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given an equation, p = n + k + m

Solving for n, we get

n = p - k - m

Hence, In the given equation, n = p - k - m

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Answer:

(8, 9 000)

Step-by-step explanation:

Answer:

1. 1

2. 1

Step-by-step explanation:

Step 1

recall the eqn of a line y = mx + c

where m is the slope

step 2

compare you eqn given with the eqn y = mx + c

y = mx + c

y = 1 x + 17

then m = 1 which is slope.

both qns follows the same procedure

If a country's public debt in 2009 was $11,982,000,000,000 and its budget for 2010 was $101,347,000,000 in deficit, the public debt in 2010 is $12083347000000.

As given

if the public debt of a country in 2009 was $11,982,000,000,000 and the budget for 2010 was in deficit by $101,347,000,000 .

Total public debt in 2010 = Public debt in 2009 + Amount by which 2010 budget deficit .

= $ 11982000000000 + 101347000000

= $ 12083347000000

Therefore the public debt in 2010 is $12083347000000.

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The graph that represents the equation y - 4.5 = 2.5(x - 5) is the third graph

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, y - 4.5 = 2.5(x - 5).

y - 4.5 = 2.5x - 12.5.

y = 2.5x - 8.

Now, to determine the graph we'll choose some random values of x for which we'll have different values of y.

When x = - 1 , y = - 10.5 ⇒ (-1, -10.5 ).

When x = 0 , y = - 8 ⇒ (0, - 8).

When x = 1 , y = -5.5 ⇒ (1, -5.5).

When x = 2 , y = -3 ⇒ (2, -3).

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