One year, the population of a city was 102,000. Several years later it was 110,160. Find the percent increase.

Bearing is a topic that deals with angles and distance. Thus, the required answers to the given question are:

i. Distance of 1034.2 miles

ii. Bearing of [tex]158^{o}[/tex]

The speed of an object is the rate of movement of the object with time.

speed = [tex]\frac{distance}{time}[/tex]

So that:

distance = speed x time

i. In the given question; let the initial distance covered be represented by d, so that:

d = 250 x 2

  = 500 miles

ii. Let the second distance covered by the pilot be represented by D, so that:

D = 300 x 2

   = 600 miles

iii. Thus let the distance to the starting point be represented by x. From Cosine rule, we have:

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2abCos C

[tex]x^{2}[/tex] = [tex]500^{2}[/tex] + [tex]600^{2}[/tex] - 2(500 x 600)Cos [tex]140^{o}[/tex]

   = 250000 + 360000 - 600000(-0,7660)

   = 610000 + 459600

   = 1069600

x = [tex]\sqrt{1069600}[/tex]

  = 1034.22

x = 1034.2 miles

Using the Sine rule to determine the required internal angle, we have:

[tex]\frac{a}{Sin A}[/tex] = [tex]\frac{c}{Sin C}[/tex]

[tex]\frac{500}{Sin A}[/tex] = [tex]\frac{1034.22}{Sin 140}[/tex]

Sin A = [tex]\frac{500*0.6428}{1034.22}[/tex]

         = 0.3108

A = [tex]Sin^{-1}[/tex] 0.3108

   = 18.11

A = [tex]18^{o}[/tex]

To determine angle B, we have:

140 + 18 + B = 180 (sum of angles in a triangle)

158 + B = 180

B = 180 - 158

  = 22

B = [tex]22^{o}[/tex]

Thus, the required bearing is 180 - 22 = 158

Therefore the distance and bearing required to fly to starting point are 1034.2 miles and [tex]158^{o}[/tex] respectively.

Learn more about bearing of a given point at https://brainly.com/question/24340249

#SPJ1

Answer:

  $348.79

Step-by-step explanation:

You want to know Sandy Sellers' net weekly pay if she earns $15 per hour for 30 hours' work and has deductions of ...

Sellers' net pay will be her gross pay, less the taxes. Those taxes are all percentages of her gross pay.

  gross pay = (hourly rate) × (hours worked)

  gross pay = ($15.00/hour) × (30 hours) = $450

The deductions from her pay total ...

  12% +2.84% +6.2% +1.45% = 22.49% . . . . of her gross pay

The dollar amount of the deductions is ...

  0.2249 × $450 = $101.205 ≈ $101.21

Then Sellers' net pay is ...

  net = gross - deductions

  net = $450 -101.21 = $348.79

Sandy Sellers' take-home pay each week is $348.79.

The coordinates of the endpoints after the transformation is (c) (7, 3) and (1, 5)

From the question, we have the following parameters that can be used in our computation:

Segment with endpoints at (1, 5) and (7, 3)

Also from the question, we have:

The points are reflected the segment about a vertical line through the segment’s own midpoint

When this is done, this means that the points would swap positions

So, we have the following representations

(1, 5) and (7, 3) ⇒ (7, 3) and (1, 5)

Hence, the coordinates of the endpoints is (c) (7, 3) and (1, 5)

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

Answer:

Parabola

Step-by-step explanation:

A conic section is a curve obtained by the intersection of a plane with the surface of a (double-napped) cone, When the plane is parallel to the edge of one cone.

Thus, The intersection is a parabola.

Answer: degenerate hyperbola

Step-by-step explanation:

degenerate hyperbola because its the thickest of the plane so it can be formed.

Ty's visibility if out the upper window of a building with an altitude of 1,602 feet is 49.

What is altitude?

The height of an object in relation to a planet's or a natural satellite's surface, like sea level or land. the degree to which a celestial body is elevated above the horizon.

Here, we have

Given

The formula V = 1.225 √a is used to estimate how far a person can see on a clear day, where V is the visibility in miles and A is the altitude in feet.

We have to find Ty's visibility out the upper window of a building with an altitude of 1,602 feet.

We know that

V = 1.225 √a

a = 1,602 feet.

V = 1.225 √1602

V = 49

Hence, Ty's visibility out the upper window of a building with an altitude of 1,602 feet is 49.

To learn more about the altitude from the given link

https://brainly.com/question/28786198

#SPJ1

In linear equation, 96 is the quotient.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                             Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

f(x) =  6x^3-+18x^2-18x+12

x - 2 = 0

x = 2

f( x) = 6 * 8 + 18 * 4 - 18 * 2 + 12

     =  48 + 72 - 36 + 12

      = 132 - 36

      = 96

Learn more about linear equation

brainly.com/question/11897796

#SPJ1

If log₁₀2=0.3010, the value of  log₂10 will be 3.3×10⁻⁴.Logarithm identity is used to find the value of the log₂10.

It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

[tex]\rm a^b = c\\log_ac =b[/tex]

It is given that, log₁₀2=0.3010

We have to find the log₂10

The following logarithm identity is used as,

logₐn=logₙa

log₂10 =1/ log₁₀2

log₂10 =1/ 0.3010

log₂10 =3.3×10⁻⁴

Thus, if log₁₀2=0.3010, the value of  log₂10 will be 3.3×10⁻⁴. Logarithm identity is used to find the value of the log₂10.

Learn more about the Logarithm here:

brainly.com/question/163125

#SPJ1

Answer:10

Step-by-step explanation:10 times two is twelve and minus 2 is ten.

The revenue function of Patrice Bergeron earnings is R(x) = (50 + 5x)(20 -x)

From the question, we have the following parameters that can be used in our computation:

Charges  = $50

Students = 20

Also, we have:

For every $5/hr he increases the price, he loses one student.

This means that

Charges  = 50 + 5x

Students = 20 - x

So, the revenue equation is

R(x) = Charges * Students

Substitute the known values in the above equation, so, we have the following representation

R(x) = (50 + 5x)(20 -x)

Hence, the function is R(x) = (50 + 5x)(20 -x)

Read more about revenue functions at

https://brainly.com/question/12983911

#SPJ1

Complete question

Whenever he is injured and unable to play, Patrice Bergeron likes to earn a little extra cash by doing some tutoring. He currently charges $50/hr and has 20 students that he works with. He has discovered that for every $5/hr he increases the price, he loses one student.

What is the revenue function

B. There is no function rule

If the midpoint of AB is at (0,4). and A = (3,0) then B is at point (-3, 8)

The formula to determine the center point of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.

The formula is of the form

X= (x₂ - x₁)/2

Y = (y₂ - y₁)/2

solving for B (x₂, y₂)

0 = (x₂ + 3)/2

0 = x₂ + 3

x₂ = -3

4 = (y₂ + 0)/2

8 = y₂ + 0

y₂ = 8

point B = (-3, 8)

Learn more about midpoint  here:

https://brainly.com/question/5566419

#SPJ1

s = 1, x = 0, y = 3 and s = 1, x = 2, y = 0 produce an image congruent to its pre-image so option C and D are correct

What is dilation?

Dilation is the increase or decrease in the size of a figure by a scale factor. Rigid transformations preserve the shape of a figure. Examples of rigid transformation are reflection, rotation and translation.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation. The phrase "scale factor" describes this transition.

Dilation is said to be a rigid transformation if the scale factor is equal to one.

Therefore the dilation by a scale factor of one produce an image congruent to its pre-image.

Find out more on dilation at: brainly.com/question/3457976

#SPJ1

Answer:

-9

Step-by-step explanation:

-3+-6=-9

Answer: A

Step-by-step explanation:

From the statement.

Times = Multiplication

The sum of a number and 18.3 = (r + 18.3)

Equals = 27.9

Therefore,

-6 x (r + 18.3) = 27.9

Answer: 9 because 45% of 20 is 9

The line passes through Y=5. Correct option is A.

Two lines are perpendicular to each other if they are at right angle

to each other.

Given, line is perpendicular to Y-axis and passes through (-4,5).

Therefore, the given line is parallel to X-axis and passes Y-axis at y=5.

Hence, the given line passes through Y=5.

To learn more about perpendicular lines visit:

https://brainly.com/question/2096532

#SPJ1

Answer: x=3√14

Step-by-step explanation:

Answer:

[tex]\huge{\boxed{\text{A) move the decimal point one place to the right}}}}[/tex]

Step-by-step explanation:

Think about the following scenarios

4.00 * 10

529.00 * 10

4 * 10 = 40 (4.00 * 10 =  40.0)

529 * 10 = 5290 (5290.00 * 10 =  5290.0)

As you can see, the decimal point is moving one space to the right when multiplying by ten.

In the decimal system, moving the decimal point one place to the right multiplies by ten, while moving the decimal point one place to the left multiplies by 1/10.

Hope it helps :) and let me know if you want me to elaborate.

If a graph G has an Euler path, then it must include precisely two odd vertices. Or, to put it another way, G cannot have an Euler path if the number of odd vertices is less than 2.

To learn more about Euler path refer to:

https://brainly.com/question/11598226

#SPJ1

Answer:

  a.  $3155.19

  b.  $1,135,868.40

  c.  $705,868.40

  d.  interest

Step-by-step explanation:

You want to find the monthly payment, total repaid, and finance charge on a 30-year mortgage for $430,000 at the rate of 8%.

You can use a spreadsheet, financial calculator, app, or the amortization formula to find the payment amount.

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

where P is the principal amount of the loan, r is the annual interest rate, and t is the number of years.

  A = 430,000(0.08/12)/(1 -(1 +0.08/12)^(-12·30)) ≈ 3155.19

The monthly payment is $3,155.19.

The total of the 12·30 = 360 payments is ...

  360 · $3155.19 = $1,135,868.40

It will take about $1,135,868.40 to pay off the loan.

The finance charge is the difference between the amount repaid and the original loan amount:

  $1135868.40 -430000 = $705,868.40

The finance charge is $705,868.40.

The finance charge at $706k is considerably greater than the original cost of the home, $430k.

The finance charge is greater.

For many of the rolls die, the long run relative frequency of a number less than 3 landing face up is 1/3.

What is relative frequency?

The proportion of outcomes where a specific event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.

Given that, Only two integers (1 and 2) are smaller than 3, hence their relative frequency will be 2/6=1/3.

The best way to interpret the data is thus,

For many rolls of the die, the long- run relative frequency of a number less than three landing face up is1/3.

Hence option A is correct which is for many of the rolls die, the long run relative frequency of a number less than 3 landing face up is 1/3.

To learn more about relative frequency visit

https://brainly.com/question/29739263

#SPJ4

The vertex labels of Δ QRT are : ∠2 label is Q, ∠8 label is T and the remaining vertex label is R. The vertex labels for ΔSTR are: ∠5 label is S, ∠9 label is R and the remaining label is T.

The polygon having three sides and three vertices are known as triangle.

If we separate the two triangles as shown in the figure. We can find the vertex labels with the help of the angles marked in the figure.

For Δ QRT, the vertex labels are:

∠2 is Q, ∠1 is R and ∠8 is T

Similarly. for ΔSTR, the vertex labels are:

∠5 is S, ∠6 is T, and ∠9 is R

Hence,  For Δ QRT, we can label as ∠2 is Q, ∠1 is R and ∠8 is T and for ΔSTR we can label as  ∠5 is S, ∠6 is T, and ∠9 is R.

To learn more about triangle, use the link given below:

https://brainly.com/question/2773823

#SPJ1

Answer:

c or b

Step-by-step explanation:

For the first graph, slope = 1/5.

For the second graph, slope = -1/2.

For the third graph, slope = 2.

For the fourth graph, slope = 1.42.

What is the slope of the line?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

                  [tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

For the first graph, the coordinates will be (-15, 0) and (0, 3)

          Slope = 3 - 0/0-(-15)

                     = 3/15

            Slope = 1/5

For the second graph, the coordinates will be (0, 5) and (10, 0)

          Slope = 0 - 5/10- 0

                     = -5/10

            Slope = -1/2

For the third graph, the coordinates will be (2.5, 0) and (0, -5)

          Slope = -5-0/0 - 2.5

                     = -5/-2.5

            Slope = 2

For the fourth graph, the coordinates will be (-2.8, 0) and (0, 4)

          Slope = 4 - 0/0 - (-2.8)

                     = 4/2.8

            Slope = 1.42

Hence,

For the first graph, slope = 1/5.

For the second graph, slope = -1/2.

For the third graph, slope = 2.

For the fourth graph, slope = 1.42.

To learn more about the slope of the line, visit:

https://brainly.com/question/16949303

#SPJ1

Answer:

88.75% is the percentage Tami earned.

Answer:

x + y = 87

1.5x + 0.5y = 78.50

Step-by-step explanation:

Let x be the number of nachos sold and y be the number of sodas sold

x nachos will cost 1.50x dollars
y sodas will cost 0.50y dollars

So total sales = 1.5x + 0.5y and we know he made $78.50

so one equation is
1.5x + 0.5y = 78.50

Total sold = x + y and we know that this number is 87

So the second equation is

x + y = 87

A circle is a two-dimensional figure with a radius and circumference of

2πr.

The arc length of AB is 10.05.

A circle is a two-dimensional figure with a radius and circumference of

2πr.

We have,

The radius of the circle = 12

The circumference of the given circle.

= 2πr

This means,

The whole circle is 360°.

= 360/360 x 2πr

= 2πr

Now,

We need to find 48°

So,

The arc length of AB.

= 48/360 x 2πr

= 48/360 x 2 x 3.14 x 12

= 48/30 x 2 x 3.14

= 10.048

Rounding to the nearest hundredths.

= 10.05

Thus,

The arc length of AB is 10.05.

Learn more about circle here:

https://brainly.com/question/11833983

#SPJ1

Answer: 10.05

Step-by-step explanation:

The arc length of AB.

= 48/360 x 2πr

= 48/360 x 2 x 3.14 x 12

= 48/30 x 2 x 3.14

= 10.048

Rounding to the nearest hundredths.

= 10.05

The arc length of AB is 10.05.

Answer:155m

Step-by-step explanation:GK is congruent to HI

The inequality that the graph represent is y < -x + 1. The correct option is B. y < –x + 1

From the question, we are to determine the inequality that represents the given graph.

From the given information,

The line is passing through the coordinates (1, 0) and (-1, 2).

Using the formula for the equation of a line,

Using the formula,

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

Then,

(y - 0)/(x - 1) = (2 - 0)/(-1 - 1)

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

y/(x -1) = -1

y = -1(x -1)

y = -x + 1

Since the line is dotted and the shaded region is below the line, the inequality becomes

y < -x + 1

Learn more on Determining the inequality that represents a graph here: https://brainly.com/question/28342666

#SPJ1