Shirley returned from Canada with $23 445 and converted the dollars to kina at the Jacksons International Airport Calculate the amount in kina he received at rate of exchange of K1 (2 marks) CASO 4689 ?​

Answer: 100.48 cubic feet

Step-by-step explanation:

[tex]\sf Length\, of\,the\,field=\boxed{\sf 104(m)}}.[/tex]

A conversion factor is just a fraction that contains an equivalence. We make the numerator be the unit we want to have as a result and the denominator is the current unit that we have.

The problem states that 0.5 cm equals 8 m, and we want to convert from cm to m, therefore, a conversion factor for this problem is:

[tex]\sf \dfrac{8(m)}{0.5(cm)}[/tex]

To use the conversion factor, just multiply each measure by the fraction:

[tex]\sf 6.5(cm) \dfrac{8(m)}{0.5(cm)}[/tex]

Here the centimeters (cm) cancel out each other and the ending answer is expressed in meters:

[tex]\sf 6.5(cm) \dfrac{8(m)}{0.5(cm)}=\boxed{\sf 104(m)}.[/tex]

For the other measure:

[tex]\sf 3.25(cm) \dfrac{8(m)}{0.5(cm)}=\boxed{\sf 52(m)}.[/tex]

So a soccer field, as you may already know, is always longer than it is wide, therefore, the greatest measure (104m) should be the length of the field.

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Answer:

9) 36     36  and   36 (all three sides equal)

10) 3.1    3.1  and  3.3  (two sides equal)

Step-by-step explanation:

#9

This is an equilateral triangle so all three sides are equal
Expressions for two of the sides are 6y and 4y + 12

Set these expressions equal to each other and solve for y:
6y = 4y + 12
6y - 4y = 12
2y = 12
y =6

So the side with expression 6y becomes 6 · 6 = 36

Since it is an equilateral triangle, each of the three sides is 36

#10
This is an isosceles triangle with side 2x + 1.7 = x + 2.4

Solve for x:
2x + 1.7 = x + 2.4

2x - x = 2.4 - 1.7
x = 0.7

So the side with x + 2.4 = 0.7 + 2.4 = 3.1 same as the side with 2x + 1.7

The third side with 4x + 0.5 = 4(0.7) + 0.5 = 2.8 + 0.5 = 3.3

So the sides of this triangle are 3.1, 3.1 and 3.3

As per the given variables, the rate at which they earn credits is 8 credits per semester

Total number of credits = 19

Total number of semesters = 6

Credits after six semesters = 67

Calculating the change in credits -

Change in credits -

Credits after six semesters - Inital credits

= 67  - 19

= 48 credits

Total time = 6 semesters

Calculating the change in credits over the six semesters and dividing by the total time to get the pace at which the college student is acquiring credits.

Therefore, the rate at which the college student is earning credits is:

Rate = Change in credits / Total time

= 48 credits / 6 semesters

= 8 credits per semester

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Answer:

m = 3

Step-by-step explanation:

Given:

[tex]2^{m-3}[/tex] = 1

Take the logarithm of both sides (logarithm of 1 is 0):

m - 3 = 0

Add 3 to both sides:

m - 3 + 3 = 0 + 3

m = 3

Hence, m = 3.

Logarithm is the power to which a number must be raised in order to get some other number. For example:

The value of the expression "(x²y - 2z)/4", when x = 12 , y = 8 and z = 6, is (c) 285.

An "Expression" is defined as a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation, which are written using mathematical symbols and follow certain rules.

We have to evaluate the expression : (x²y - 2z)/4, if x = 12 , y = 8 and z = 6,

To evaluate , we substitute x = 12 , y = 8 and z = 6, in the expression,

So, We have,

⇒ (12² × 8 - 2×6)/4,

⇒ (144 × 8 - 12)/4,

⇒ (144 × 8 - 12)/4,

⇒ (1152 - 12)/4,

⇒ 1140/4,

⇒ 285,

Therefore, the value of the given expression, when x=12, y=8, and z=6, is 285, the correct option is (c).

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The equation expressing d as a function of t can be found by using the formula for distance traveled with constant speed:

d = vt

where d is the distance, v is the constant speed, and t is the time elapsed.

In this case, the speed is 150 cm/s, so the equation is:

d = 150t

To find the total distance traveled in meters at t = 2 seconds, we need to first find the total distance traveled in centimeters at t = 2 seconds:

d = 150t

d = 150(2)

d = 300 cm

To convert to meters, we divide by 100:

d = 300/100

d = 3 meters

Therefore, at t = 2 seconds, the object has traveled a total distance of 3 meters.

Answer:

[tex](x-2)(x+16)[/tex]

Step-by-step explanation:

Use graphing calculator and find the x-intercepts.

Answer:

4mn + 3m + 8n + 6 = (m + 2)(4n + 3)

The missing term is 4n.

Answer:

43.7 x 0.25 is 10.925

Step-by-step explanation:

To multiply decimals, we can use the following steps:

1. Multiply the numbers as if they were whole numbers, ignoring the decimal points.

2. Count the total number of decimal places in the factors being multiplied. This will be the number of decimal places in the product.

3. Place the decimal point in the product so that it has the same number of decimal places as the total counted in step 2.

Using these steps, we can find the product of 43.7 and 0.25 as follows:

1. 437 x 25 = 10925

2. There are two decimal places in 43.7 and two decimal places in 0.25, so there are a total of four decimal places in the factors being multiplied.

3. Place the decimal point in the product so that it has four decimal places: 10.925

Therefore, the value of 43.7 x 0.25 is 10.925.

The equation of the line parallel to the graph of 2x - 3y = 7 and containing the point (-3,-3) is y = (2/3)x - 1.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation of the graph: 2x - 3y = 7.

First, we need to rearrange the given equation into slope-intercept form (y = mx + b) by solving for y:

2x - 3y = 7

-3y = -2x + 7

y = (2/3)x - 7/3

The slope of the given line is 2/3.

Hence, any line parallel to it will also have a slope of 2/3.

Using the point-slope form, we determine the equation of the line that passes through (-3,-3) and has a slope of 2/3:

y - y1 = m(x - x1)

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

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

y = (2/3)x - 1

Therefore, the equation of the line is y = (2/3)x - 1.

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Answer: x=4, sides = 12, 8, 6, 8

Step-by-step explain

Perimeter means the sum of all sides of a shape, in this example there are four sides add the sides and set it equal to 34.

X+8+x+4+2x-2+x²-2x=34

x²+2x+10=34

x²+2x-24

(x-4)(x+6)

x=4, x=-6

x can not be -6 because then the x+4 side would be -2, therefore it is extraneous and x=4 is the correct answer.

Now to find side lengths just plug in 4 for x

4+8=12

4+4=8

2*4-2=6

4*4-2*4=8

Answer:

157,000

Step-by-step explanation:

π r² h

An expression for the exact area of each shaded region in the figure include the following:

Shaded area = area of the regular hexagon - area of the regular pentagon  + area of the square - area of the equilateral triangle.

In Mathematics and Geometry, the area of a regular polygon can be calculated by using the following formula:

Area of a regular polygon = (n × s × a)/2

Where:

Based on the diagram (see attachment), the area of the first shaded region is given by;

Area of first shaded region = Area regular hexagon - Area regular pentagon

For the area of the second shaded region, we have;

Area of second shaded region = Area of a square - Area of the equilateral triangle

Therefore, the total area of all of the shaded regions is given by;

Total shaded area = {area of the regular hexagon - area of the regular pentagon} + area of the square - {area of the equilateral triangle}.

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The probability that a student is a graduate student given they are a history major is approximately 0.16.

The likelihood or chance that an event will occur is quantified by probability. A number between 0 and 1, where 0 denotes that the occurrence is impossible and 1, denotes that the event is certain, is generally used to express it.

We are given the following information:

Total number of students who are history major: 463

Total number of graduate students: 261

Number of graduate students who are history major: 73

We can use the formula for conditional probability to find the probability that a student is a graduate student given that they are a history major:

P(graduate | history) = P(graduate and history)/P(history)

P(graduate | history) = 73/463

P(graduate | history) ≈ 0.1575 (rounded to the nearest hundredth)

Therefore, the probability that a student is a graduate student given they are a history major is approximately 0.16.

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Answer:

26

Step-by-step explanation:

Answer:

5.2 seconds

Step-by-step explanation:

To get one foot, we need to divide by 5.5

Set up a proportion:

[tex]\frac{5.5}{5.5}=\frac{28.6}{5.5}[/tex]

Solve:

[tex]1ft.=5.2secs.[/tex]

The trigonometry functions when evaluated are shown below

In trigonometry, sine (sin), cosine (cos), and tangent (tan) are three basic functions that relate angles to the sides of a right triangle.

They are defined as follows:

sin A = opposite side/hypotenuse.

cos A = adjacent side/hypotenuse.

tan A = opposite side/adjacent side.

So, we have

Figure 1

Figure 2

Figure 3

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A negative correlation may be seen on the graph. The birth rate declines over time. This indicates that the number of births per 1000 persons in the US has been declining over time.

Answer:

16

Step-by-step explanation:

5y/3x = 5

3x = 5y/5

3x = y

3x + 2y = 36

y + 2y = 36

3y = 36

y = 36/3

y = 12

3x = y

3x = 12

x = 12/3

x = 4

x + y

= 4 + 12

= 16

x + y = 16

Answer:

x = 7.9 (nearest tenth)

y = 24.6° (nearest tenth)

Step-by-step explanation:

Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

As we have been given the lengths of both legs of the right triangle, we can use Pythagoras Theorem to find the length of the hypotenuse, x:

[tex]\begin{aligned}3.2^2+7^2&=x^2\\10.24+49&=x^2\\59.24&=x^2\\x^2&=59.24\\x&=\sqrt{59.24}\\x&=7.6967525...\\x&=7.9\; \sf (nearest\;tenth)\end{aligned}[/tex]

Therefore, x = 7.9.

[tex]\hrulefill[/tex]

The tangent ratio is a trigonometric ratio that relates the angle of a right triangle to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]

As we have been given the lengths of the sides that are opposite and adjacent angle y, we can use the tangent trigonometric ratio to find the measure of angle y:

[tex]\begin{aligned}\tan(y)&=\dfrac{3.2}{7}\\y&=\tan^{-1}\left(\dfrac{3.2}{7}\right)\\y&=\vphantom{\dfrac12}24.5671713...^{\circ}\\y&=24.6^{\circ}\;\sf (nearest\;tenth)\end{aligned}[/tex]

Therefore, y = 24.6°.

The probability of Casey selecting a tie that goes well with the sport coat is 0.517.

The probability of Casey selecting a tie that does not go well with the sport coat is 0.483

The probability of Casey selecting a tie that goes well with the sport coat is:

P(goes well) = 15/29

P(goes well) ≈ 0.517

The probability of Casey selecting a tie that does not go well with the sport coat is:

P(does not go well) = 1 - P(goes well)

P(does not go well) = 1 - 15/29 = 14/29

P(does not go well) ≈ 0.483

The odds in favor of the tie going well with the sport coat are:

P(goes well) : P(does not go well) = 15/29 : 14/29

P(goes well) : P(does not go well) = 15:14

The odds against the tie going well with the sport coat are:

P(does not go well) : P(goes well) = 14/29 : 15/29

P(does not go well) : P(goes well) = 14:15

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The dimensions of the rectangular block indicates;

(a) The largest number of bricks that can be cut from the block is 48 bricks

(b) The volume of the wood left is 216 cm³

The volume of the rectangular block is the product of the length, L, width, W, and height, H.

1. The dimensions of the rectangular block indicates that the block volume is; V = 24 cm × 9 cm × 7 cm = 1,512 cm³

The largest number of bricks that have side lengths of 3 cm that can be cut from the block is therefore;

Number of cubes; (24)/3 × (9)/3 × (7)/3 ⇒ 8 × 3 × 2 = 48

(b) The volume of wood left = 1512 - 48 × 3 × 3 × 3 = 216

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Answer:

[tex]f(0) = 6.2 \sqrt{4.5} + 18 = 31.2[/tex]