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Step-by-step explanation:

The earth is 40000 kilometers around. There is no need to round off because the circumference already contains significant figures.

How do I calculate a circle's circumference?

A circle's diameter is multiplied by to determine its circumference (pi). You can also determine the circumference by multiplying 2radius by pi (=3.14).

Given: theta angle (central) = 7.2°; arc length S = 800 km

This indicates that an 800 km long arc is extending a circle with a 7.2° center angle ( earth in this case).

By definition, "An arc's length is a portion of a circle's diameter."

Therefore, we must first establish what percentage of the circle the specified arc length represents.

360° is a complete circle.

Thus, the fraction equals 7.2°/360°, or 1/50.

As a result, the stated arc length (800km) with a 7.2° central angle is 1/50th of the entire circle.

Thus, the whole circumference is 800 x 50, or 40000 km.

Alternately, you can calculate circumference using the formula below:

360° center angle x arc length as the circumference (theta)

Values substituted: circumference 800 = 360° 7.2°

circumference = 360°, 800°, and 7.2°, or 40000 kilometers

Therefore, the earth is 40000 kilometers around. There is no need to round off because the circumference already contains significant figures.

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Maya drove on the mountains for her trip. Due to traffic, her average rate of miles per hour was faster at the time of coming back to her home than going on her trip. Thus, The distance between where she lives and the mountains is

288 miles .

Let's consider that Maya live x miles from the mountains.

Let her rate to mountains be y miles/h.

we have given that

Driveing time taken by Maya going from home to trip location= 9 hours due to traffic

total return time taken by her = 4 hours

average rate = 40 miles/hour

Using rate formula,

Rate = distance/time

=> distance (d) = rate (r) × time (t)

so, x/y = 9

=> x=9y --(1)

Return trip 4 hours then rate = y+40

=> x/(y+40) =4 --(2)

using Substitution method, x= 3 substitute in (2)

=> 9y/(y+40)=4

=> 9y=4y+160

=> 9y-4y=160

=> 5y=160

=> y= 160/5

=> y=32

Now, x=9y

x=9×32= 288 miles

Hence, distance to the mountain is 288 miles.

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Complete question:

Maria drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 9 hours. When Maria drove home, there was no traffic and the trip only took 4 hours. If her average rate was 40 miles per hour faster on the trip home, how far away does Maria live from the mountains?

Do not do any rounding.

By using trigonometry, it can be calculated that

Value of x is 23.775

What is trigonometry?

Trigonometry shows the relationship between sides and angles of a right angled triangle.

There are six trigonometrical functions. They are

[tex]sin \theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]

[tex]sin\theta = \frac{perpendicular}{hypotenuse}[/tex]

[tex]cos\theta = \frac{base}{hypotenuse}[/tex]

[tex]tan\theta = \frac{perpendicular}{base}[/tex]

[tex]cot\theta = \frac{base}{perpendicular}[/tex]

[tex]sec\theta = \frac{hypotenuse}{base}[/tex]

[tex]cosec\theta = \frac{hypotenuse}{perpendicular}[/tex]

Trigonometry is a very important tool in mathematics.

Here, trigonometry is used

From the figure,

cos 18 = [tex]\frac{x}{25}[/tex]

0.951 = [tex]\frac{x}{25}[/tex]

x = 0.951 [tex]\times[/tex]25

x = 23.775 cm

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Complete Question

what is the value of x in this triangle? enter your answer in the box. x

x = cm

A right triangle. The hypotenuse is labeled as 25 centimeters. The base is labeled as x. The alternate base angles are labeled as right angle and 18 degrees, respectively.​

Answer:

57671680x^9 y^2

Step-by-step explanation:

using combinatorics

Tim will use 5/24 kilograms of raisins in his trail mix.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Tim has 1(¹/₄) kilogram of raisins. He uses 1/6 of the raisins in his trail mix.

The weight of the raisins will be calculated as,

Weight = 1(¹/₄) x 1 / 6

Weight = ( 5 / 4 )  x ( 1 / 6 )

Weight = 5 / 24 kg

Therefore, Tim will use 5/24 kilograms of raisins in his trail mix.

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The average time of the Olympic speedskated is 43.29 units.

An average, which is frequently the sum of the numbers divided by the total number of the numbers in the group, is a single number that is selected to describe a group of numbers in simple English.

For example, the average of the numbers 2, 3, 4, 7, and 9 is 5.

The four sorts of averages that we recognize are mean, mode, median, and range.

Although the others are our most popular "measures of central tendency," range is actually a measure of spread or distribution.

So, the average time is calculated as follows:

We have: Time: 44.64,43.45,42.79 and 42.28

The formula for average mean: ∑ₓ/n

Where ∑ₓ is the sum of observations and n is the number of observations.

Now, calculate the average time:

Average = 44.64+43.45+42.79+42.28/4

Average = 173.16/4

Average = 43.29

Therefore, the average time of the Olympic speedskated is 43.29 units.

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The linear equation written in the slope-intercept form is:

y = -x - 5

A linear equation can be written in the slope-intercept form as:

y = m*x + b

Where m is the slope and b is the y-intercept.

Particularly, if the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope of the line is written as:

m = (y₂ - y₁)/(x₂ - x₁)

Here we can use the first two points on the table (or any you want) to find the slope:

(-1, -4) and (3, -8)

m = (-8 + 4)/(3 + 1) = -1

The slope is -1, so the line is something like:

y = -x + b

To find the value of b we can use another of the points on the table, if we use (7, -12) then we must have:

-12 = -7 + b

-12 + 7 = b

-5 = b

The linear equation is:

y = -x - 5

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Answer:

The answer should be 12.5%

Answer: a=0

Step-by-step explanation:

-2a + 5a = -3a

3a = -3a

a= 0

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at 0.1 level of significance, we can conclude that these data are sufficient to indicate that the mean for population 2 is larger than that for population 1.

For the null hypothesis

H0: μd ≥ 0

For the alternative hypothesis

H1: μd < 0

The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 10 - 1 = 9

The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = (- 3.7 - 0)/(2.71/√10)

t = - 4.32

We would determine the probability value by using the t test calculator.

p = 0.00097

Since alpha, 0.1 > than the p value, 0.00097, then we would reject the null hypothesis. Therefore, at 0.1 level of significance, we can conclude that these data are sufficient to indicate that the mean for population 2 is larger than that for population 1.

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Answer:

So...

Step-by-step explanation:

He earns $7.00 per hour, and he needs $210.00. H represents hours.

7.00 every hour

So 7.00 x  2 is 14

7.00 x 10.00 is 70

7.00 x 30 is 210. So after 30 hours he will be able to buy his phone. He should buy his phone on black friday. But now its too late.

Calculations in mechanics involving masses dispersed in space, such as the linear and angular momentum, benefit from using the centre of mass as a reference point.

The centre of mass of the trapezoid can be found by breaking it into two trapezoids and finding the centre of mass of each. The centre of mass of the first trapezoid is located at (3, 5). The centre of mass of the second trapezoid is located at (9, 5). Therefore, the centre of mass of the trapezoid is located at (6, 5).

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Answer:

  see attached

Step-by-step explanation:

You want a graph of the piecewise function ...

[tex]f(x)=\begin{cases}x&\text{if $x\le -1$}\\-3x+2&\text{if $-1 < x < 4$}\\4&\text{if $x\ge 4$}\end{cases}[/tex]

The graph is attached.

For x ≤ -1, the graph is a line with slope 1. If it were allowed to continue, it would pass through the origin. It terminates in a closed dot at (-1, -1)

For -1 < x < 4, the graph is a line with slope -3 through point (0, 2) on the y-axis. It has open circles at both ends, at points (-1, 5) and (4, -10).

For x ≥ 4, the line is horizontal at y=4. It has a closed dot at (4, 4).

__

Additional comment

The dot at the end of an interval is closed if the "or equal to" case is included (≤ or ≥). If it is not (< or >), then the dot is an open circle.

The slope is the ratio of "rise" to "run". It is the number of grid squares the line moves up (+) or down (-) for each grid square to the right.

Answer:

5

Step-by-step explanation:

 25/5 = 5/1 = 5

The number of ways 3 courses can be selected is 3654.

What are the Permutation and Combination?

Permutations and combinations are the various ways in which objects from a set can be selected to form subsets, generally without replacement. When the order of selection is a factor, this selection of subsets is called a permutation; when it is not, it is called a combination.

Total no. of courses available = 29

Courses needed to graduate = 3

No of ways these courses can be selected:

                    = ²⁹C₃

                    = 29!/ [(29-3)! - 3!]

                    = 29! / 26! 3!

                    = 29 * 28 * 27 * 26!/ 26! 3*2

                    = 29* 14* 9

                    = 3654

So, the number of ways 3 courses can be selected is 3654.

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Answer: $342

Step-by-step explanation:

We take 162.00 divided by 9 = $18 / h

To find the salary of 19 hours we just need to take 18 times 19 = $342

Answer: -8r^13

Step-by-step explanation: We just need to take those numbers multiplied by each other. -4 timed 2 = -8. r^5 timed r^8 = r^13, we just add both because they have the same base and multiple a square is the same as adding them together.

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Answer:

7.5

Step-by-step explanation:

W -- X -- Y ----- Z

We are given that :

Given this we want to find XZ

XZ consists of XY and YZ so we must find the length of the individual segments.

Finding YZ

Here, we know that YZ = WY as y is the midpoint of WZ. If WY = 5 then YZ also = 5

Finding XY

Given that WY = 5 and that X is a midpoint of WY we know that the segments WX and XY = WY and are congruent.
In other words we can say that 2XY = WY

==> WY = 5

2XY = 5

==> divide both sides by 2

XY = 2.5

Finding XZ

Again, XY + YZ = XZ

We have XY = 2.5 and YZ = 5

Hence, 2.5 + 5 = XZ

XZ = 7.5

Answer:

XZ = 7.5

Step-by-step explanation:

A drawing is sometimes very helpful.

Start by drawing a segment with endpoints W and Z.

   +--------------------------------------------+

   W                                                  Z

Y is the midpoint of WZ. Draw point Y in between W and Z and the same distance from both W and Z.

    +---------------------+--------------------+

   W                        Y                       Z

X is the midpoint of WY. Draw X between W and Y, and the same distance to W and Y.

   +----------+----------+--------------------+

   W          X           Y                       Z

Because of the midpoints, we know that:

WX = XY

WY = YZ

WY = 5

WX and XY are each half of WY, so WX = XY = 5/2 = 2.5

WY = YZ = 5

XZ = XY + YZ

XZ = 2.5 + 5

XZ = 7.5

The perimeter of the window to the nearest hundredth will be;

⇒ 102.8 cm

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The shape of window is semicircle.

And, The radius of window (r) = 20 cm

Now,

We know that;

The perimeter of semicircle = πr + 2r

Here, The radius of window (r) = 20 cm

So, We get;

The perimeter of the window = πr + 2r

                                             = 3.14 x 20 + 2 x 20

                                             = 62.8 + 40

                                             = 102.8 cm

Thus, The perimeter of the window to the nearest hundredth will be;

⇒ 102.8 cm

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Answer:

Step-by-step explanation:

x^2 + y^2 = z^2 is the pythagorean theorem.

If you divide the large triangle into two separate ones, with sides 7, 4 and 0.5y, you can use the pythagorean theorem to figure out 0.5y. So:

7^2 = 4^2 +(0.5y)^2

49-16 = 33

so y=2sqrt(33)

Subtract full rotations of 2π until the angle is greater than or equal to 0 and less than 2π

sec(π4) – trigonometry value

The exact value of trigonometry - sec(π4) is 2√2.

Multiply 2√2 by √2.

2⋅√2⋅2

Combine and simplify the denominator.

2√2

Cancel the common factor of 2.

√2

There are various ways to display the outcome.

Exact Form:

√2

Decimal Form:

1.41421356…

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The measure of angle WZY of the Trapezoid WXYZ is; 37

We are told that the Trapezoid WXYZ is isosceles. This means that there would be two angles that are equal.

Thus, we can see that Side WZ and XY are equal and as such, it means that Angle WZY is congruent to angle XYZ.

We are told Angle WZY measures (8x – 3) and angle XYZ measures (7x + 2). Thus;

(8x – 3) = (7x + 2)

8x - 7x = 2 + 3

x = 5

Thus;

Angle WZY = (8(5) – 3)

Angle WZY = 37°

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Answer:

[tex]12m^2-71m+99[/tex]

Step-by-step explanation:

I will use distributive property

(4m-9)(3m-11)

4m(3m)+4m(-11)-9(3m)-9(-11)

12m^2-44m-27m+99

Combine like terms

12m^2-71m+99

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The sampling distribution for a goodness of fit test is the

A continuous distribution with degrees of freedom is a chi-square distribution. It is used to describe how a sum of squared random variables is distributed.

When comparing categorical variables from a random sample, the statistical test known as chi-square is used to assess the degree of fit between the predicted and actual results.

We can therefore conclude that chi-square distribution is the sampling distribution for a goodness of fit test

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The solution of the system of equations:

y = x + 422

y + 4  =x

is the point (-88, -46)

Here we have the system of equations:

y = x + 42

2y + 4  =x

To solve the system, we can replace the first equation into the second one:

2*(x + 42) + 4 = x

2x + 84 + 4 = x

2x + 88 = x

2x - x = -88

x = -88

And the value of y is:

y = x + 42

y = -88 + 42 = -46

The solution is the point (-88, -46).

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A. Using the distance formula, we can state that the opposite sides are congruent because AD = BC = √10 units and AB = CD = √40 units.

B. The diagonals are equal, AC = BD = √50 units.

C. Based on the slopes of each side, there are 4 right angles on the rectangle.

The distance formula is used to find the distance that exist between tow points that are on a coordinate plane. The formula is: d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

What is the Slope of a Line?

Slope = change in y / change in x.

A. The coordinates of each of the vertices of the rectangle are:

A(1, 2)

B(7, 4)

C(8, 1)

D(2, -1)

Use the distance formula to find AB, CD, BC, and AD.

AB = √[(7−1)² + (4−2)²]

AB = √40

CD = √[(2−8)² + (−1−1)²]

CD = √40

BC = √[(8−7)² + (1−4)²]

BC = √10

AD = √[(2−1)² + (−1−2)²]

AD = √10

Therefore, the opposite sides are congruent because AD = BC = √10 units and AB = CD = √40 units.

B. The diagonals are AC and BD. Find their lengths using the distance formula:

AC = √(8−1)² + (1−2)²]

AC = √50 units

BD = √[(2−7)² + (−1−4)²]

BD = √50 units

Therefore, the diagonals are equal, AC = BD = √50 units.

C. Find the slope of AB, CD, BC, and AD:

Slope of AB = change in y / change in x = rise/run = 2/6 = 1/3

Slope of CD = 2/6 = 1/3

Slope of BC = -3/1 = -3

Slope of AD = -3/1 = -3

-3 is the negative reciprocal to 1/3, this means that, if the two lines that meet at a corner have these two slope, then they will form a right angle because they are perpendicular to each other.

Therefore, there are 4 right angles on the rectangle.

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Answer:

The ratio of mangos to grapes is 2:7.

Step-by-step explanation:

The original ratio of mangos to grapes would be 4:14. When it says mangos to grapes, it means mangos first, then grapes. If it said grapes to mangos, the grapes would go first. But, in this case the mangos go first. Now, we don't worry about the strawberries because it says to find the ratio of mangos to grapes, which is 4:14. Now, it says to simplify it to the simplest form. So, we can do this by dividing both numbers by the same number down as far as they can go as a whole number (a number without a decimal):

4 ÷ 2 = 2

14 ÷ 2 = 7

So, this is as far as we can go. So, our final answer is 2:7.

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Answer:

2:7

Step-by-step explanation:

4 mangos for every 14 grapes

the ratio right now is 4:14 this can be simplified by dividing by 2

4 divided by 2 = 2        ( 2 x 2 = 4 )

14 divided by 4 = 7       ( 7 x 2= 14)

Now the ratio is 2:7, or 2 mangos for every 7 grapes we know this is right because in order to use the amount the recipe calls for you need to double the answer

(adding separately is easier)

2+2 = 4

7+7 = 14

= 4:14

The line segments joining the given points are not parallel.

In order to find the slope of a line, calculate the angle it makes with x axis as a reference. Then its slope can be determined by taking tan ratio of that angle.

Given that,

The first segment is joined from (3, -3) to (3, 9).

And, the second segment is joined from (-5, 12) to (1, 0).

In order for the segments to be parallel, their slope must be equal.

The slopes of both the segments can be found as,

First segment,

Slope = (3 - 3)/(-3 - 9)

          = 0/-12

          = 0

Second segment,

Slope = (-5 - 1)/(12 - 0)

          = -6/12

          = -1/2

Since slopes of the segments are not equal, they are not parallel.

Hence, the given line segments are not parallel.

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