Allison heads out on a three day sailing trip. On the first day, she sails 45 miles east and 15 miles north. On the second day,
she leaves from the exact location she ended the day before and makes it 35 miles east and 30 miles south. On the third
day, she gains another 15 miles east and 55 miles south. At the end of her final day, how far is she from her initial starting
point? Round your answer to the nearest whole number.

43 yards because she spent 9.03 cents on ribbon 9.03 divided by 0.21=43

As per the distance concept, the speed of the buses are 79 km/h and 69km/h if the two buses leave a station at the same time and travel in opposite directions.

Distance

Distance refers the physical length or an approximation based on other physics or common usage considerations.

Given,

Two buses leave a station at the same time and travel in opposite directions. One bus travels 10 slower than the other. If the two buses are 276 miles apart after 2 hours,

Here we need to find the rate of each bus.

Let us consider the speed of the first bus is x km/h.

Then the speed of the other bus = (x - 10) km/h

We know the formula of distance is,

Distance = time × speed

When we combined speed then we get,

=> x + x - 10 = (2x - 10) km/h

=> 2(2x - 10) =276

When we expand the equation, then we get,

4x - 40 = 276

4x = 316

After calculating,

x = 79 km/h

The speed of first bus x = 79 km/h

Speed of the second bus = x - 10 = 79 - 10 = 69 km/h

Therefore, the speed of the buses are 79 km/h and 69/km/h if the two buses leave a station at the same time and travel in opposite directions.

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total 4023 pages the 27 students read by the end of December

Step-by-step explanation:

35 + 38+35+41 = 149

27 students

149 × 27

4023 pages 27 students reads in this given four month

Based on the information given, below statements are true

A. Feldman & Sons have a greater hourly rate.

B. The graph of the function for Strong Arm Movers has a greater y-intercept than the graph of the function for Feldman & Sons.

Feldman and Sons have a higher hourly rate or slope (35  compared to 25), but Strong Arm.  Movers have a higher y-intercept (50  compared to 30). Feldman and Sons charge more than  Strong Arms for both 3-hour and 2.5-hour transfers.

Movers is an organization that helps people pack and move their belongings from one place to another. They take full responsibility for the items we have asked them to move and they also offer refunds if anything is broken or lost. That's what  packers and movers mean. Movers and packers pack goods. Material load. Movement of goods and unloading of goods.

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Answer:[tex]26cm^{2}[/tex]

Step-by-step explanation: To do this you have to dissect the shapes into singular shapes.

First, you do the parallelogram at the bottom. 4×2

Then the middle rectangle. 3×4

Then the triangle at the top. 4×3÷2

Area= [tex]26m^{2}[/tex]

a. The expected value is 0.40

b. The standard error is 0.0024

Given that:

Sample size, n=100

Population proportion, p=0.40

a) The expected value of the sample proportion is defined as:

E(^p)=p

now,

E(^p)=0.40

b) The standard error of the sample proportion is defined as:

SE(^p) = √p(1-p)/n

SE(^p) = √0.40(1-0.40)/100

SE(^p) = 0.0024

c) The sampling distribution of the sample proportion is normally distributed with the expected value of the sample proportion of 0.40.

Therefore,

E(^p) = 0.40

d) The central limit theorem states that the sample statistic (sample proportion) tends to the population parameter (population proportion) as the sample size tends to infinity (OR n→∞).

^P~N(p, p(-p)/n) as n→∞

Hence we get the required answers.

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The approximate value of the height f the tree when the base diameter is 3.2 meters is 119.47 meters

From the question, the equation  of the function of height is given as

h = 35d²/3

Also from the question, we have the base diameter of the fir tree to be

d = 3.2m

Next, we substitute 3.2 for d in the equation of the function of height given as

h = 35d²/3

So, we have the following equation:

h = 35 x 3.2²/3

Evaluate the exponent

So, we have

h = 35 x 10.24/3

Evaluate the product

So, we have the following equation:

h = 358.4/3

Evaluate the quotient

This gives

h = 119.47

Hence, the height is 119.47 meters

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Answer:

Step-by-step explanation:

5 parts blue

yellow: 3 parts

WE SHOULD HAVE DONE EQUAL COLOURS FOR A GOOD RESULT?

The linear equation which can be used to represents Curtis weekly salary is S = 8H + 0.02C

Weekly salary = Curtis wage per hour(Hours Worked) + Percentage commission(Commission earned on total sales)

S = 8(H) + 2%(C)

S = 8H + 0.02(C)

S = 8H + 0.02C

So therefore, Curtis linear equation for his weekly salary is S = 8H + 0.02C

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The equation of the line is y = -3x + 8.

The slope of a line, or angle between it and the horizontal, is stated numerically. The slope of a line, ray, or line segment in analytical geometry is the ratio of its vertical to horizontal distance between any two locations ("slope equals rise over run").

Given,

x1 = 1

y1 = 5

m = -3

From,

y-y1 = m(x-x1) (x-x1) (x-x1)

y - 5 = -3(x - 1) (x - 1) (x - 1)

y-5 = -3x + 3

y = -3x + 8

As a result, the equation for the line is y = -3x + 8.

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In order to determine how many packages of diapers you can buy, it is only necessary to divide the total money you have, between the price of each package.

You have:

available money = 40$

package cost = 8$

Then, you calculate the quotient between available money and package cost:

Hence, you can buy 5 packages of diapers with 40$

Answer: 7.5

Step-by-step explanation: 2 x 7.5 = 15  

     3 + 6 - 15  

         9 -15

            -6

From the expression we can see that it is translated 3 units downwards from the origin.

The price of 1 yard of blue fabric and 1 yard of green fabric is obtained by solving the system of linear equations and it is $8

Let

x = price of blue fabric per yard

y = price of green fabric per yard

"The blue fabric costs $2 more per yard than the green fabric" means:

x = y + 2  (Equation 1)

" LaTanya buys 6 yards of blue fabric and 9 yards of green fabric and pays $57" means:

6x + 9y = 57  (Equation 2)

Substitute equation 1 into equation 2:

6x + 9y = 57

6 (y + 2) + 9y = 57

6y + 12 + 9y = 57

15 y = 45

y = 3

Substitute y = 3 into equation 1

x = 3 + 2 = 5

Hence, the price of blue fabric is $5 per yard while the green fabric is $3 per yard.

The price of 1 yard of blue fabric and 1 yard of green fabric = x + y = 3 + 5 = $8

Complete question:

LaTanya buys 6 yards of blue fabric and 9 yards of green fabric. The blue fabric costs $2 more per yard than the green fabric. She pays a total of $57. What would be the combined cost of 1 yard of blue fabric and 1 yard of green fabric?

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Answer:

Slope = (6/1) or 6

Step-by-step explanation:

(0, -1), (1, 5)

(x₁, y₁)  (x₂, y₂)

        y₂ - y₁          5 - (-1)        5 + 1          6

m = ------------- = ------------- = ---------- = -------

        x₂ - x₁           1 - 0             1              1

y - y₁ = m(x - x₁)

y - (-1) = 6(x - 0)

y + 1 = 6x - 0

  -1            -1

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

y = 6x - 1

I hope this helps!

The angles in each of the four quadrants with a common reference to the acute angle 41° are as follows;

It follows from the task content that the angles which have a common reference to the angle 41° in each quadrant he determined.

On this note, the angles can be determined from custom formulas for reference angles in each quadrant as follows;

Ultimately, the angles in each quadrant with a common reference alongside 41° are; 139°, 221° and 319°.

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120 children and 120 adults were admitted to the amusement park if the admission fee collected was $1980.00

The number of children and adults that entered the park can be calculated using linear equations.

Considering x to be the number of adults and y to be the number of children;

As 240 people entered the park, therefore;

x + y = 240

As the fee for children is $3.50 and for adults is $13, therefore;

13x + 3.50y = 1980

Determining the value of y in the first equation;

x + y = 240

y = 240 - x

Putting this value of y in the second equation;

13x + 3.50y = 1980

13x + 3.50(240 - x) = 1980

13x + 840 - 3.50x = 1980

9.5x = 1980 - 840

9.5x = 1140

x = 1140 / 9.5

x = 120

To determine the value of y, we Substitute this value of x in the first equation;

y = 240 - x

y = 240 - 120

y = 120

Hence, 120 children and 120 adults entered the park if the admission fee for children was $3.50 and for adults was $13.00

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The correct option regarding whether this is an exponential or linear function is given as follows:

This is a linear function because there is a common difference in the balance between the weeks.

The function will be linear or exponential depending if there is a common difference or a common ratio between the terms, as follows:

From the given table, the differences are given as follows:

The differences are the same, hence it is a linear function and the correct option is:

This is a linear function because there is a common difference in the balance between the weeks.

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Answer:

The correct answer is (C) This is a linear function because there is a common difference in the balance between the weeks.

Step-by-step explanation:

The person up top is correct

Answer:

Touchdowns: 6

Field goals: 3

PATS: 5

Step-by-step explanation:

6*6 = 36

3*3 = 9

5*1 = 5

9+5+36 = 50 points

6+3+5 = 14 scored times

Answers:

6 touchdowns (TD)

3 field goals (FG)

5 points after touchdown (PAT)

===============================================

Explanation:

Acronyms used in football

Define the following variables

"They had 3 more touchdowns than field goals", so,

TD = FG + 3

x = y + 3

They scored 14 times which means we can say

x+y+z = 14

Let's look at the point breakdown per type of score

Then we can add up those expressions to get us to 6x+3y+1z = 50 points total. This is the same as saying 6x+3y+z = 50.

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

Here's our system of equations

x = y+3

x+y+z = 14

6x+3y+z = 50

Let's replace each x with y+3 in the second equation. Then solve for z.

x+y+z = 14

y+3+y+z = 14

2y+z = 14-3

2y+z = 11

z = 11-2y

Now replace every x with y+3 in the third original equation

6x+3y+z = 50

6(y+3)+3y+z = 50

6y+18+3y+z = 50

9y+z = 50-18

9y+z = 32

Then plug in z = 11-2y and solve for y

9y+z = 32

9y+11-2y = 32

7y+11 = 32

7y = 32-11

7y = 21

y = 21/7

y = 3 is the number of FGs scored

Use this to find z

z = 11-2y

z = 11-2(3)

z = 11-6

z = 5 is the number of PATs scored

Now let's find x

x = y+3

x = 3+3

x = 6 is the number of TDs scored

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

Checking the answers:

x+y+z = 6+3+5 = 9+5 = 14 times they scored

6x+3y+z = 6*6+3*3+5 = 36+9+5 = 50 points scored

There are 3 more TDs than FGs since x = y+3 leads to 6 = 3+3 which is a true statement.

All three original equations we set up for the system of equations are true. Therefore, the final answers are confirmed.

Answer: [tex]f(4)=8[/tex]

Step-by-step explanation:

The Remainder Theorem states, "If a polynomial [tex]p(x)[/tex] is divided by the binomial [tex]x-a[/tex], the remainder obtained is [tex]p(a)[/tex]."

In this case, we are given the polynomial [tex]f(x)[/tex], and the polynomial [tex]f(x)[/tex] is divided by the binomial [tex]x-4[/tex]. If you were to plug in [tex]4[/tex] for [tex]x[/tex] in [tex]f(x)[/tex], you would get [tex]f(4)=8[/tex] as a result of the binomial theorem.

Given, the perimeter of the rectangular billboard, P=42 m.

The length of the rectangular billboard is 9 m more than the width.

Let l be the length and w be the width of the rectangular billboard.

Then, the length can be expressed as,

The perimeter of a rectangle can be expressed as,

Now, put l=9+w and P=42 m in the above equation to find w.

Hence, the length is,

Therefore, the length of the rectangular billboard is 15 m and the width of the rectangular billboard is 6 m.

Answer: £7.20

Step-by-step explanation: £5.76/64 = £0.09 So one pen is £0.09. If you need 80, then £0.09 x 80 = £7.20

The population for which 78% is a legitimate estimate of the percent of people that are 'very satisfied" with the yoga classes is C. anyone who has taken a yoga class at the gym in the past year but not before that.

An estimate is a rough calculation that may not be based on real figures or it may be based on rounded-off or appropriated facts and figures.

Estimates enable the decision-maker to make a quick guess or decision that cannot wait for all the facts to be collected.

Thus, the population of interest for the estimate includes members and non-members who have participated.

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Answer:

D

Step-by-step explanation:

By evaluating the equation in x = 2030, we can estimate the price to be $51.60.

We know that the equation:

y = 1.67*x - 3338.5

Models the relationship between the year, x, and the average ticket price of a Miami Marlins baseball ticket.

We know that this relationship works for the years 2006 to 2021, but can be used to estimate the price for years after and before that.

if we use x = 2030, we will get:

y = 1.67*2030 - 3338.5 = 51.6

This will be the price, in dollars, of a game in the year 2030.

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Answer:

y = x - 11

Step-by-step explanation:

The trigonometric ratios of the right triangle are as follows:

A right triangle is a triangle that has one of its angles as 90 degrees.

The side and angles of a right triangle can be solved using trigonometric ratios.

The ratios of the sides of a right triangle are called trigonometric ratios.

A right angle triangle has the opposite side, adjacent side and hypotenuse side depending on the angles location.

Using ratios,

sin ∅ = opposite / hypotenuse

cos ∅ = adjacent / hypotenuse

tan ∅ = opposite / adjacent

Therefore,

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