A triangle with side lengths of 200 meters, 300 meters, and 250 meters is shown. a surveyor measures the lengths of the sides of a triangular plot of land. what is the measure of the angle of the triangular plot at which the surveyor stands? approximate to the nearest degree. cos–1(0.75) = 41° cos–1(0.125) = 83° cos–1(0.563) = 56° cos–1(0.15) = 89°

The expression that is equivalent to the given statement was reduced.

The given expression is:

[tex]\frac{(3m^{-2}n)^{-3} }{6mn^{-2} }[/tex]

Some important power rules are:

[tex](ab)^n=a^nb^n[/tex]

[tex](a^{m} )^n=a^{mn}[/tex]

[tex]a^m.a^n=a^{m+n}[/tex]

[tex]\frac{a^m}{a^n} =a^{m-n}[/tex]

[tex]a^{-m} =\frac{1}{a^m}[/tex]

So, the given expression can be written as:

[tex]\frac{3^{-3} m^{6} n^{-3} }{6mn^{-2} }[/tex]

=[tex](\frac{3^{-3} }{6} )*(\frac{m^{6} }{m} )*(\frac{n^{-3} }{n^{-2} } )[/tex]

=[tex](\frac{1}{3^{3} *6} )*m^{5} *(\frac{1}{n^{3} *n^{-2} } )[/tex]

=[tex]\frac{m^5}{162n}[/tex]

Hence, the expression that is equivalent to the given statement was reduced.

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Answer: All real numbers greater than or equal to -5

Step-by-step explanation:

The vertex has a y coordinate of -5, and all the other outputs are more than -5.

Answer: Below:

Step-by-step explanation:

Mean: (5+7+3+6+8+5+6+4+15)/9 = 6.55555 ≅6.56

Median: 6

Mode: 5, 6

Range: 12

Answer:

The answer is C. 2.94

Step-by-step explanation:

All you have to do is take 588 and divide it by 200 which gives you the answer of 2.94.

Answer:

C. addition property

Step-by-step explanation:

they wouldve had to add 36 to both sides of the equation, so addition

Answer:

side lengths: 12 feet, 9 feet, 4 feet

Step-by-step explanation:

Conditions for unique triangles with 3 sides:

9 + 6 = 15

As 15 < 18 this is NOT a unique triangle

9 + 4 = 13

As 13 > 12 this IS a unique triangle

3 + 2 = 5

As 5 < 6 this is NOT a unique triangle

14 + 4 = 18

As 18 < 24 this is NOT a unique triangle

i think the answer is this

Answer:

As Per Provided Information

Diameter of Garden 12 yards

Radius of Garden will be 12/2

Radius of Garden will be 6 cm

We have been asked to find the area of the circular garden .

Formula Used here

[tex] \underline{\boxed {\bf \: Area_{(Garden)} \: = \pi {r}^{2}}} [/tex]

Just put the value and let's calculate the area of circular garden .

[tex] \qquad \longrightarrow\sf \: Area_{(Garden)} \: = 3.14 \times {6}^{2} \\ \\ \\ \qquad \longrightarrow\sf \: Area_{(Garden)} \: = 3.14 \times 36 \\ \\ \\ \qquad \longrightarrow\sf \: Area_{(Garden)} \: = 113.04 \: {yard}^{2} [/tex]

Therefore,

Step-by-step explanation:

Given :-

We have to find the area of garden

Area of Circle = πr²

Putting the known values ,

Area = 3.14 × 6² yd²

Area = 113.04 yd²

The distance between you and train 1 at time t is

20.6 km + (0.2 km/h) t

and the distance between you and train 2 at time t is

59.7 km - (2.1 km/h) t

The trains are an equal distance away from you when

20.6 km + (0.2 km/h) t = 59.7 km - (2.1 km/h) t

Solve for t :

(2.3 km/h) t = 39.1 km

t = 17 h

at which point they are

20.6 km + (0.2 km/h) (17 h) = 24 km

away from you.

Answer:

Below in bold.

Step-by-step explanation:

a) The volumes will be in the ratio of the cubes  of the edges.

So volume of A / volume B = 20^3 / 5^3

Volume A / 25 = 8000/125

Volume a = (25* 8000) / 125

= 8000/ 5

= 1600 cm^3.

b) ratio of the surface area of A to surface area of B

=  20^2 : 5^2

= 400:25

= 16:1.

c. The volume of pyramid B is 25 cm*3 so it' height is  25 / area of its base = 25/5^2

= 1 cm.

Now its slant height = √(1^2 + (2.5)^2)

= √7.25

= 2.6926 cm

So surface area = 25 + 4 * 1/2 * 5 * 2.6926

= 51.926

= 51.93 cm^2 to nearest hundredth.

and the surface area of pyramid B = 51.926 * 16

= 830.82 cm^2 to nearest hundredth.

Answer:

b

Step-by-step explanation:

Answer:

The correct answer is B, because B. is a compression of 6 and x, with 6 added in just like they said in the question.

Answer:

£28.8 Milllion

Step-by-step explanation:

£30,000,000 × 0.8 = £24,000,000 (Depreciates by 20%)

£24,000,000 × 1.2 = £28,800,000 (Appreciates by 20%)

Answer:

D

Step-by-step explanation:

If you are solving for something like this, set the given full integer equal to x times the percent given

Step-by-step explanation:

I guess you mean it is

12 cm long, 4cm wide and 5 cm high.

and the fabric goes outside on the box ? strange, but ok.

a box (like a die) has 6 sides in the form of 3 pairs of equal rectangles :

top-bottom, left-right, front-back

the surface area is the sum of all 6 rectangles.

top-bottom :

2 × 12×4 = 2 × 48 = 96 cm²

left-right :

2 × 4×5 = 2 × 20 = 40 cm²

front-back :

2 × 12×5 = 2 × 60 = 120 cm²

in total

120 + 40 + 96 = 256 cm²

Answer:

A

Step-by-step explanation:

The actual price is 13.6% lower than the expected price.

CPI or Consumer Price Index is a measure of determining retail inflation in an economy, based on price variations in a fixed basket of goods and services, over overtime periods.

Let's suppose the expected price is x.

The percent relation of the actual price of a winter hat to the expected price is given by;

CPI = ( expected price ) : ( price in 1983 ) × 100

219  =  ( x  : 12.95 ) × 100

Divide both sides by 100.

x : 12.95 = 2.19

x =2.19 × 12.95

x = $28.36 ( expected price )

p = ( 24.50 × 100 ) / 28.36

p= 2450/28.36

p = 86.4 %

100 % - 86.4 % = 13.6 %

Hence, the actual price is 13.6% lower than the expected price.

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Answer:

297.99

Step-by-step explanation:

367.99-45-25=297.99

Answer:

Negative Correlation

Step-by-step explanation:

The plot looks like it's going downwards. If it was an equation, it'd be something with y = -x +b.

Using it's concept, it is found that there is a [tex]\frac{3}{16}[/tex] probability that George will choose a white pair of shoes and a pair of socks that are not white.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem:

Since the events are independent:

[tex]p = \frac{1}{4} \times \frac{3}{4} = \frac{3}{16}[/tex]

[tex]\frac{3}{16}[/tex] probability that George will choose a white pair of shoes and a pair of socks that are not white.

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Answer:

112 customers will pay cash next week

Step-by-step explanation:

1,100/138=7.97= approximately 8

Multiply the amount of customers who paid cash, 14 by 8.

Answer:

20 cm²

Step-by-step explanation:

Look at the diagram attached.

If the height is 4cm, we will have two sides that are 4cm for our rectangle.

We can label the other sides as x.

They are both x since opposite sides of a rectangle are equal in length.

We can make an equation with our perimeter:

[tex]2(4) + 2(x) = 18\\8 + 2x = 18\\2x = 10\\x = 5[/tex]

Now that we know the length & height, we can calculate the area:

4 × 5 = 20 cm²

Answer:

he will have 29 nickles

Step-by-step explanation:

I just solved it on paper, hope it helps and if it's right

Answer:

Step-by-step explanation:

Remark

If the entire circle was shaded the radius sweeping out the circle would go through 360 degrees.

So the way to solve this problem is to multiply the entire area of the circle by (81/360)

Area of the sector = (81/360) * pi * r^2

pi = 3.14

r =8.91 cm

Area of the sector = (81/360) * 3.14 * 8.91^2

Area of the sector = 56.09

Rounded to the nearest tenth, the answer is 56.1

Answer: 56.1 cm^2

Answer:

2x² + 7x + 3 = 0

Step-by-step explanation:

[tex]\sf \text{Sum = -3 + $(\dfrac{-1}{2})$}[/tex]

                    [tex]\sf = \dfrac{-3*2}{1*2}-\dfrac{1}{2}\\\\=\dfrac{-6}{2}-\dfrac{-1}{2}\\\\=\dfrac{-7}{2}[/tex]

[tex]\sf \text{Product =$-3*\dfrac{-1}{2}$}[/tex]

                         [tex]= \dfrac{3}{2}[/tex]

Quadratic polynomial:

[tex]\boxed{x^{2}-sum *x+product = 0}[/tex]

[tex]x^{2}- \left(\dfrac{-7}{2}\right)x+\dfrac{3}{2}=0\\\\x^{2} + \left(\dfrac{7}{2}\right)x+\dfrac{3}{2}=0\\[/tex]

Multiply the entire equation by 2

[tex]2*x^{2} + 2*\dfrac{7}{2}x +2*\dfrac{3}{2}=0[/tex]

2x² + 7x + 3 = 0

[tex]2 {ab}^{2} + {8a}^{2} b[/tex]

[tex]2ab(b + 4a)[/tex]

to factorise first, find the highest common factor of each of the terms in the expression then, write the highest common factor (HCF) in front of any brackets atlast, fill in each term in the brackets by multiplying out.

The value of the expression after factorization will be;

⇒ 2ab (b + 4a)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 2ab² + 8a²b

Now,

Factorize the expression as;

⇒ 2ab² + 8a²b

⇒ 2ab × b + 2×2×2a×a×b

⇒ 2ab (b + 4a)

Thus, The value of the expression after factorization will be;

⇒ 2ab (b + 4a)

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Answer:

$2.56

Step-by-step explanation:

12.80 ÷ 5 = 2.56