Which box-and-whisker plot best represents the information from the data?
10 12 15 19 22 22 23 26 30 32​

Answer:

Options (B) and (D)

Step-by-step explanation:

If a triangle is a 30° - 60° - 90° triangle, measure of the angle between the leg and hypotenuse will be either 60° or 90°.

Therefore, by applying Cosine rule in the given options.

c² = a² + b² - 2abCosC

All the given options are the right triangles.

[Since they follow the Pythagoras theorem]

Option (A),

Angle between the sides having measures 3 and 5 units,

4² = 3² + 5² - 2(3)(5)CosC

16 = 9 + 25 - 30.CosC

30.CosC = 18

[tex]C=\text{Cos}^{-1}(\frac{5}{6} )[/tex]

C = 33.56°

Therefore, this triangle is not a 30-60-90 triangle.

Option (B),

Angle between the sides measuring 5 and 10 units,

[tex](5\sqrt{3})^2=5^2+10^2-2(5)(10)\text{CosC}[/tex]

75 = 125 - 100(CosC)

Cos(C) = 0.5

C = 60°

Therefore, other angles of the triangle will be 30° and 90°.

And it's a 30°-60°-90° triangle.

Option (C),

10, 10, 10√2

It's a right triangle and the measure of legs are equal.

Since legs of this sides are equal, angles opposite to these equal sides will be equal.

Sum of all interior angles = 180°

m∠A + m∠B + m∠C = 180°

If m∠B = 90°

m∠A + 90° + m∠C = 180°

2(m∠A) = 90°

m∠A = 45°

Therefore, the given sides make a 45°- 45°- 90° triangle.

Option (D).

Angle between the sides 3 and 6,

(3√3)² = 3² + 6² -2(3)(6)CosC

27 = 9 + 36 - 36.(CosC)

CosC = [tex]\frac{18}{36}[/tex]

C = [tex]\text{Cos}^{-1}(\frac{1}{2})[/tex]

C = 60°

Therefore,

These sides make a 30°- 60°- 90° triangle.

Options (B) and (D) are the 30°- 60°- 90° triangle.  

Answer as a fraction = 1/25

Answer in decimal form = 0.04

Answer in percent form = 4%

Explanation:

There are 5*5 = 25 different outcomes, of which only one outcome has 5,5. The probability of picking two 5s is 1/25 = 0.04 = 4%

Answer:

4%

Step-by-step explanation:

Answer:

We know that our triangle has one side along the line:

y = (1/4)*x

And other side along the line:

y = -(1/4)*x.

Now, we want to find the vertex.

And we know that the vertex is the point where the two sides conect, so the vertex must be a common point of both lines.

Then we have:

y = (1/4)*x = -(1/4)*x

x = -x

The only solution to that equation is x = 0.

now we evaluate our lines in x = 0 and get:

y = (1/4)*0 = 0

y = -(1/4)*0 = 0

Then the lines intersect in the point (0, 0)

Then the vertex must be in the point (0, 0)

Answer:

Answer:

The equivalent expression for this equation is x²¹ × y⁻²¹

Step-by-step explanation:

When you are multiplying exponents that are in parentheses, you multiply the exponential numbers together. So, for this problem, we will multiply the exponents together so we can get our final equivalent expression.

(x⁻³ × y³)⁻⁷

So, we will multiply -3 by -7 and we will also multiply 3 by -7 because those are our exponential numbers.

x²¹ × y⁻²¹

So, this is the final expression that is equivalent to our equation.

The expression (x⁻³.y³)⁻⁷ is equivalent to x ²¹ . y ⁻²¹.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

The given expression is,

(x⁻³.y³)⁻⁷

To find the solution for the expression,

Simplify the power terms,

x⁽⁻³ˣ⁻⁷⁾ . y ³ˣ⁻⁷

x ²¹ . y ⁻²¹

The simplified form of the expression (x⁻³.y³)⁻⁷ is x ²¹ . y ⁻²¹.

Hence, option (A) is correct.

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Answer:

3x^2

Step-by-step explanation:

Given:

(3x) * {(1/x)^-4 }* (x^-3)

=(3x) * {1 ÷ (1/x)^4} * {1/x^3}

=(3x) * {1(x/1)^4} * (1/x^3)

=(3x) * (x^4) * (1/x^3)

=(3x) (x^4) (1) / x^3

Multiply the denominators

=3x^5 / x^3

Can also be written as

=3*x*x*x*x*x / x*x*x

Divide the x

= 3*x*x / 1

=3x^2

Answer:

AEB and  CED

Step-by-step explanation:

Given the two pairs of congruent sides, you now use the vertical angles as the pair of congruent included angles, <AEB and <DEC.

The congruent triangles are:

AEB and  CED

Answer:

B-   Triangle AEB and triangle CED

Step-by-step explanation:

I took the test and it was correct

Answer:

(x+3)(x-2)

Step-by-step explanation:

We can immediately see that there are roots at x = -3, and x = 2.

Because the website gives us that this in the form of (x + _) (x - _), our anwser is (x+3)(x-2)

oops I just saw your comment. Too late i guess...

Answer:

f(x)=1(x+3)(x-2)

Step-by-step explanation:

Answer:

about 62m^3

Step-by-step explanation:

Answer:

The distance of  Musah's final point from the center in the west direction is   60.355 steps

The distance of  Musah's final point from the center in the north direction is   85.355 steps

Step-by-step explanation:

Given that :

Musah stands at the center of a rectangular field.

He takes 50 steps north, then 25 steps West and finally 50 on a bearing of 315°.

The sketch for Musah's movement is seen in the attached file below.

How far west is Musah's final point from the centre?

In order to determine how far west  is Musah's,

Let d be the distance of how far west;

Then d = BC + CD cos θ

In the North West direction,

cos θ = cos 45°

d = 25 + 50( cos 45°)

d = 25 + 50([tex]\dfrac{1}{\sqrt{2}}[/tex]  )

d = 25 + 50( 0.7071)

d =25 + 35.355

d = 60.355 steps

How far north is Musah's final point from the center?

Let d₁ be the distance of how far North;

Then d₁ = AB + CD sin  θ

d₁ = 50 + 50  sin  45°

d₁ = 50 + 50([tex]\dfrac{1}{\sqrt{2}}[/tex]  )

d₁ = 50 + 50( 0.7071)

d₁ = 50 + 35.355

d₁ = 85.355  steps

Answer:

215483 cm³

Step-by-step explanation:

Formula for volume of a cylinder = πr² · h

radius = 1/2diameter

1. Set up the equation

(3.14)(15²)(305)

2. Solve

215482.5

rounded to the nearest cubic centimeter = 215483 cm³

Answer:

215483 cm³

Step-by-step explanation:

credit goes to person up top

Answer:

y=3

Step-by-step explanation:

Answer:

25.4 cm

Step-by-step explanation:

will make it simple and short

2*b + 2*h

2*4.5 + 2*8.2 = 25.4 cm

Hey there! I'm happy to help!

The perimeter is the distance around the rectangle.

In a rectangle, there are two pairs of opposite sides, and those opposite sides are equal. They are known as the length and the width.

In a rectangle, you have two sides that have the same length and two that have the same width. If you add these all up, you get the perimeter.

If our length is L and our width is W, we can write this equation.

P=2L+2W

So, we can plug in our lengths and widths to find the perimeter!

P=2(4.5)+2(8.2)

P=9+16.4

P=25.4

Therefore, our perimeter is 25.4 cm.

Have a wonderful day! Feel free to message me if you have any questions! :D

Answer:

2 Pi

Step-by-step explanation:

Notice that the shape is made of:

● 1 square with a side of 1 meter length

● 4 half-circles wich means 2 cicles with a diameter lf 1 meter.

■■■■■■■■■■■■■■■■■■■■■■■■■■

The square is inside so it isn't necessary to calculate the perimeter.

The perimeter of a circle is:

P' = d × Pi

We have 4 half-squares wich means two circles

So the total perimeter is:

● P = 2×P'

● P = 2 × d × Pi

● P = 2 × 1 × Pi

● P = 2Pi

Answer:

[tex]\boxed{ Graph. B}[/tex]

Step-by-step explanation:

Hey there!

Well slope is aka rise/run,

so starting at the red dot and rising 4 units an ruing to the right 5 units,

graph b is the correct answer.

Hope this helps :)

Graph B has a slope of 4/5.

Slope is calculated with the aid of finding the ratio of the "vertical change" to the "horizontal alternate" among (any) distinct factors on a line.

Typically, the slope of a line offers the measure of its steepness and path. The slope of an instant line among two factors says (x1,y1) and (x2,y2) may be without problems decided by finding the difference between the coordinates of the points. The slope is commonly represented by using the letter 'm'.

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Answer:

x = 6/4, or x = 3/2, OR x = 1 1/2

Step-by-step explanation:

5x - [7 - (2x-1)] = 3(x-5) + 4(x+3)

Pick one side to work on first, I will chose the right side,

Distribute on the right side.

5x - [7 - (2x-1)] = 3x - 15 + 4x + 3

Now, add like terms on the right side.

5x - [7 - (2x-1)] = 7x - 12

Now, to isolate 7 - (2x -1), subtract 5x from both sides.

so now,

-7 - (2x-1) = 2x - 12

Now, we can add 7 to both sides of the equation to isolate -(2x-1)

we add instead of subtract because the seven is a negative.

-(2x-1) = 2x - 5

Now, there is still a negative sign in front of the (2x-1), so we distribute the - to the equation.

-2x + 1 = 2x - 5

Now, we can isolate the variable and numbers bu adding five to both sides, and adding 2 to both sides. This is to make the equation easier by removing any negative terms.

6 = 4x

Divide both sides by 4

x = 6/4, or x = 3/2, OR x = 1 1/2

Answer:

The sum of the arithmetic progression is 2520

Step-by-step explanation:

The sum, Sₙ, of an arithmetic progression, AP, is given as follows;

[tex]S_{n}=\dfrac{n}{2}\cdot \left (2\cdot a+\left (n-1 \right )\cdot d \right )[/tex]

Where;

n = The nth term of the progression

a = The first term = 100

d = The common difference = -2

Given that the last term = -10, we have;

-10 = 100 + (n - 1) ×(-2)

n = (-10 - 100)/(-2) + 1 = 56

Therefore, the sum of the 56 terms of the arithmetic progression is [tex]S_{56}=\dfrac{56}{2}\cdot \left (2\cdot 100+\left (56-1 \right )\cdot (-2) \right )[/tex]

Which gives;

[tex]S_{56}={28}\cdot \left (200-\left 110 \right ) = 2520[/tex]

Answer:

[tex] \boxed{12 \sqrt{2} }[/tex]

Step-by-step explanation:

Isosceles triangle are those triangle which have two equal sides.

Perpendicular ( p ) = 12 inches

Base ( b ) = 12 inches

Hypotenuse ( h ) = ?

Now,Using Pythagoras theorem,

[tex] \mathsf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

Plug the values

[tex] \mathsf{ {h}^{2} = {12}^{2} + {12}^{2} }[/tex]

Evaluate the power

[tex] \mathsf{ {h}^{2} = 144 + 144}[/tex]

Calculate the sum

[tex] \mathsf{ {h}^{2} = 288}[/tex]

Squaring on both sides

[tex] \mathsf{h = 12 \sqrt{2} }[/tex]

Hope I helped!

Best regards!

Answer:

The upper bound is 97.5 cm

Step-by-step explanation:

The upper bound is given as the value that is larger than or equal to all values in a data set, for example, in the data set, {3, 6, 16, 23, 25}, an upper bound  is 25, however, where the accuracy of the data is given, the upper bound can be found by the following relation

Where the number is given to the nearest 100, add and subtract  half of hundred to obtain the upper bound and lower bound respectively

For the question, given that the size of the television is given as 95 cm, correct to the nearest 5 cm, we add add half of 5 cm to get the upper bound as follows;

Upper bound = 95 cm + 5/2 cm = 97.5 cm

The upper bound = 97.5 cm.

Answer:

(0, 3)

Step-by-step explanation:

First, find the slope using rise/run (y2 - y1) / (x2 - x1)

Plug in the points:

(6 - 5) / (3 - 2)

1/1 = 1

Now, we can plug in the slope and a point into the equation y = mx + b to find b (y-intercept)

y = 1x + b

5 = (1)(2) + b

5 = 2 + b

3 = b

= (0, 3)

Answer:

$6.24

Step-by-step explanation:

1 orange=%0.13

2 orange=5 green=$0.26

10 green=2 blue= $0.52

.52+.26=.78

1 red=3 blue=$0.78

0.78*8=6.24

Answer:

3(a). The ship travelled in north is 26.0 km.

(b). The ship travelled in east is 23.4 km.

4(a). The ship travelled in south is -88.61 km.

(b). The ship travelled in west is -179.29 km.

Step-by-step explanation:

Given that,

(3). Distance = 35 km

Angle = 42°

Let distance in north is y km.

We need to calculate the distance

Using vertical component

[tex]y = d\cos\theta[/tex]

Put the value into the formula

[tex]y = 35\cos42[/tex]

[tex]y=26.0\ km[/tex]

Let distance in east is x  km

We need to calculate the distance

Using horizontal component

[tex]x =d\sin\theta[/tex]

Put the value into the formula

[tex]x = 35\sin42[/tex]

[tex]x=23.4\ km[/tex]

(4). A ship sails 200 km on a bearing of 243.7°

Let distance in south is y km.

We need to calculate the distance

Using vertical component

[tex]y = d\cos\theta[/tex]

Put the value into the formula

[tex]y = 200\cos243.7[/tex]

[tex]y=-88.61\ km[/tex]

Let distance in west is x  km

We need to calculate the distance

Using horizontal component

[tex]x =d\sin\theta[/tex]

Put the value into the formula

[tex]x = 200\sin243.7[/tex]

[tex]x=-179.29\ km[/tex]

Hence, 3(a). The ship travelled in north is 26.0 km.

(b). The ship travelled in east is 23.4 km.

4(a). The ship travelled in south is -88.61 km.

(b). The ship travelled in west is -179.29 km.

Answer:

  f(x) and h(x) have the same maximum value: 3

Step-by-step explanation:

The maximum value of f(x) is 3 at (π, 3).

The maximum value of g(x) is -2 at (-3, -2).

The maximum value of h(x) is 3 at (0, 3).

Both f(x) and h(x) have the same (greatest) maximum value.

Answer:

0.555

Step-by-step explanation:

When you ask, "What is 55.5 as a decimal?", we assume you want to know what 55.5 percent is as a decimal. In other words, 55.5 percent converted to decimal.

First, we will tell you why it is useful to know 55.5 as a decimal.

Normally, to calculate 55.5 percent, you would multiply a number by 55.5 percent and then you would take the product of that and divide it by 100 to get the answer.

Instead, you can simply multiply a number by 55.5 as a decimal to get the answer.

55.5 percent means 55.5 per hundred. Therefore, to get 55.5 as a decimal, all you have to do is divide 55.5 by 100 like so:

55.5 ÷ 100 = 0.555

The solution is, as a decimal​ of 55.5% is, 0.555

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

When you ask, "What is 55.5 as a decimal?", we assume you want to know what 55.5 percent is as a decimal. In other words, 55.5 percent converted to decimal.

First, we will tell you why it is useful to know 55.5 as a decimal.

Normally, to calculate 55.5 percent, you would multiply a number by 55.5 percent and then you would take the product of that and divide it by 100 to get the answer.

Instead, you can simply multiply a number by 55.5 as a decimal to get the answer.

55.5 percent means 55.5 per hundred. Therefore, to get 55.5 as a decimal, all you have to do is divide 55.5 by 100 like so:

55.5 ÷ 100 = 0.555

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Answer:

Clarissa will take 10 hours by herself

Step-by-step explanation:

Let s = time for shawna

s-5 = time for clarissa

The formula for determining the time is

1/a + 1/b = 1/c  where a and b are the times alone and c is the time together

1/s + 1/(s-5) = 1/6

Multiply each side by 6s(s-5) to clear the fractions

6s(s-5) ( 1/s + 1/(s-5)) = 1/6 *6s(s-5)

Distribute

6(s-5) + 6s = s(s-5)

Distribute

6s -30 +6s = s^2 -5s

Combine like terms

12s -30 = s^2 -5s

Move everything to the right

0 = s^2 -5s -12s +30

0 = s^2 -17s +30

Factor

0 = ( s-15) (s-2)

Using the zero product property

s-15 =0   s-2 =0

s =15     s=2 ( This is not a reasonable answer since it is less than the time together)

s=15

s-5 = 10

Clarissa will take 10 hours by herself

Answer:

Step-by-step explanation:

4^5 is equivalent to 4^2*4*3, which, in turn, is equivalent to:

16*64 = 1024.

Also:  

8*128 = 1024, and

4*256 = 1024, and so on.

Step-by-step explanation:

[ -6 +22 – 6 + 8 ] = 18

18 ÷ (-9) = -2

{40 – (-2) -3 – ( -1)} = { 40 + 2 -3 + 1} = 40

400 ÷ 40 = 10

(40 x 23) + (40 x -17)

920 + (-680)

= 240

(1673 x 99) + 1673

1673 x 100

= 167300

Hope this helps ^-^

Converting -4 to polar form gives [tex]-4=4\exp(i\pi)[/tex].

Then the 4th roots of -4 would be the numbers

[tex]4^{1/4}\exp\left(i\dfrac{\pi+2k\pi}4\right)[/tex]

where k is taken from {0, 1, 2, 3}.

So we have

[tex]z_1=4^{1/4}\exp\left(\dfrac{i\pi}4\right)=\sqrt2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)=1+i[/tex]

[tex]z_2=\sqrt2\left(\cos\dfrac{3\pi}4+i\sin\dfrac{3\pi}4\right)=-1+i[/tex]

[tex]z_3=\sqrt2\left(\cos\dfrac{5\pi}4+i\sin\dfrac{5\pi}4\right)=-1-i[/tex]

[tex]z_4=\sqrt2\left(\cos\dfrac{7\pi}4+i\sin\dfrac{7\pi}4\right)=1-i[/tex]

Answer:

Equivalent  expression:

6a + 10

or

9a + 15

Answer:

137 votes

Step-by-step explanation:

considering an election with 681 votes and 5 candidates up for the election

dividing the votes among'st 5 candidates

= 681 / 5 = 136.2  hence the least number of first-place votes needed by a candidate using the plurality method  would be = 137 votes

136.2 + 136.2 + 136.2 + 136.2 + 136.2 = 681 ( dividing the votes equally )

136 + 136 + 136 + 136+136 = 680

hence the remaining vote = 681 - 680 = 1

least first-place vote = 136 + 1 = 137 votes