What is the interquartile range of this data set? 5,5,6,7,9,11,14,17,21,23

A. 7

B. 9

C. 11

D.13

The answer is 7.21.

Randy should attach the end of the light string approximately 7.21 feet from the base of the mast using the Pythagorean theorem, as the distance from the base to the end of the string forms the leg of a right-angled triangle with the mast and the string itself.

To solve Randy's problem, we need to use the Pythagorean theorem, which is applicable because we are dealing with a right triangle formed by the mast, the ground, and the string of lights. The mast is one leg of the triangle, and the string of lights is the hypotenuse. We are trying to find the length of the other leg, which is the distance from the base of the mast to the point where the end of the light string will be attached.

The formula for the Pythagorean theorem is:

a² + b² = c²

Where:

In this scenario, a is the mast with a known length of 12 feet, c is the string of lights with a known length of 14 feet, and b is the distance from the base of the mast we need to calculate.

By substituting the known values into the theorem, we have:

12² + b² = 14²

Which simplifies to:

144 + b² = 196

Subtracting 144 from both sides:

b² = 196 - 144

b² = 52

Then, take the square root of both sides:

b = √52

After calculating, we find that:

b ≈ 7.21 feet

So Randy should attach the end of the light string approximately 7.21 feet from the base of the mast to reach the top.

[tex]2\cdot 10^{3x}=26\\10^{3x}=13\\\log 10^{3x}= \log 13\\3x\log 10= \log 13\\3x= \log 13\\\\[/tex]

[tex]x=\frac{\log 13}{3}[/tex]

lmk if you have questions

To find the exact value of x in the exponential equation 2(10)^3x=26, divide both sides by 2, apply the common logarithm, use the power rule of logarithms, and simplify to find that x equals log(13)/3.

To solve the exponential equation 2(10)³ˣ=26 for the exact value of x using logarithms, follow these steps:

Thus, the exact value of x is log(13)/3.

The correlation coefficients from weakest to strongest negative correlation can be arranged as -0.18, -0.37, -0.52, and -0.82.

The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.

Given the correlation coefficients as -0.59 , -0.18 , -0.82 , -0.37. Now, as we know that the number closest to 1 is stronger, while the number closest to 0 is weakest. Therefore, the correlation coefficients from weakest to strongest negative correlation can be arranged as,

-0.18 < -0.37 < -0.59 < -0.82

Hence, the correlation coefficients from weakest to strongest negative correlation can be arranged as -0.18, -0.37, -0.52, and -0.82.

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Given equations : Equation A:  4y -3x =16 and

Equation B: -x-8y =3.

We are given a point (-5,0.25) plugging it in first equation

4(0.25) -3(-5) =16

1+15 =16.

16 =16 : Satisfies first equation.

Plugging (-5,0.25) it in second equation.

-(-5)-8(0.25) =3.

5 - 2 = 3.

3=3 : Satisfies first equation.

Answer: 55 meters

Step-by-step explanation:

Let the height of the building be 'h'.

Since building is standing vertical to the ground making right angle.

Then , the triangle formed is a right triangle .

The given angle of elevation : [tex]32^{\circ}[/tex]

Using trigonometry , we have

[tex]\tan\theta=\dfrac{\text{Perpendicular}}{\text{Base}}\\\\\tan(32^{\circ})=\dfrac{h}{88}\\\\\Rightarrow\ 0.6248693519=\dfrac{h}{88}\\\\\Rightarrow\ h=0.6248693519\times88=54.988502967\approx55\text{ meters}[/tex]

Hence, the approximate height of the building = 55 meters

Answer:

The answer is 16

The answer is 5.

5^2 = 25        25 - 6 = 19

5 x 2 = 10       10 + 9 = 19

7 x [tex]10^{7}[/tex]  times 14.6 x[tex]10^{5}[/tex]

Multiply 7 and 14.6 and add exponents

Final Answer 102.2 and [tex]10^{5}[/tex]

hope that helps :)

7.2 x 10 x 5 x 14.6 x 10 x 5

7.2 x 100000 x 14.6 x 100000

720000 x 1460000 = 1.0512 x 10 x 12

ANSWER

[tex]x=10[/tex]

and

[tex]y=20[/tex]

EXPLANATION

Since corresponding angles are equal,

[tex]4x+y=60---(1)[/tex]

Alternate angles are also equal, therefore,

[tex]8x+y=100---(2)[/tex]

Equation (2) minus equation (1) gives,

[tex]\Rightarrow 4x=40[/tex]

[tex]\Rightarrow x=10[/tex]

We put [tex]x=10[/tex] in to equation (1)

[tex]4(10)+y=60[/tex]

[tex]y=60-40[/tex]

[tex]y=20[/tex]

To find x and y in the violin string diagram, use the properties of angles formed by transversals and parallel lines. Corresponding angles and interior angles are key relationships. In the example, x = 15° and y = 90°.

The problem involves understanding the relationships between angles formed by transversals and parallel lines. When a violin bow is placed across parallel violin strings, it forms transversals that create various angles.

Given that the violin strings are parallel, the interior angles formed on the same side of the transversal are supplementary. Let's consider the setup of the diagram:

Example: Suppose the violin strings and the bow are positioned in such a way that we can see the angles formed. Assume the given angles are as follows:

Step 1: Since Angle 1 and Angle 2 are corresponding angles and lie between parallel lines:

30° = 2x → 2x = 30° → x = 15°

Step 2: To find y, use the fact that the sum of angles around a point is 360°. Suppose y is opposite to the sum of Angle 1 and another given angle on the same side:

If the other angle on the same side is 60°:

y = 180° - (Angle 1 + 60°) → y = 180° - (30° + 60°) → y = 90°

Thus, the values of x and y are determined to be 15° and 90°, respectively.

The product of the expressions 3a + 5 and 6a - 2 is 18a² + 24a - 10. The distributive property is used to multiply each term in the first expression by each term in the second.

The product of the two expressions 3a + 5 and 2a + 4a - 2 can be found using the distributive property. First, combine like terms in the second expression to simplify it to 6a - 2. Now, to find the product, multiply each term in the first expression by each term in the simplified second expression:

Multiply 3a by 6a to get 18a².

Multiply 3a by -2 to get -6a.

Multiply 5 by 6a to get 30a.

Multiply 5 by -2 to get -10.

Combining these products gives you the final answer: 18a² + 24a - 10.

Answer:

$99.50

Step-by-step explanation:

Given that only if a minimum balance of 1000 dollars is maintained it will attract high interest.

To enjoy the privilege of high interest, it should be ensured that the balance does not go below 1000 dollars at any point of time.

Keeping the above in mind, we see that

Balance as of now   ..    1053 dollars

Deposit                     ..        44.50 dollars

Balance after deposit  ..   1097.50 dollars

Minimum balance        ..    1000 dollars

Maximum amount

that can be withdrawn   ..  1097.50 -1000 = 97.50 dollars.

Answer:

it is a linear one i think

The classification of angles 1 and 4 as either linear pairs, vertical angles or neither is impossible without more context or a diagram. Linear pairs are adjacent angles that form a straight line and total 180 degrees, while vertical angles are directly opposite each other from an intersection of two lines and are equal.

Without a proper diagram or more context, it's challenging to determine whether angles 1 and 4 are linear pairs, vertical angles, or neither. However, I can explain what these terms mean. Linear pairs are adjacent angles whose non-common sides form a straight line, adding up to 180 degrees. Vertical angles are angles opposite each other when two lines intersect. They are equal in measure. Unfortunately, without a specific diagram indicating the positions of angles 1 and 4, I can't definitively answer your question.

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*(The Answer)*= C. Dilation

*(Explanation)*= If you search than you will find that translation, rotation, and refection or the one that are ridged, however, dilation is.

Answer:

The correct option is 2. A dilation is NOT rigid motion transformation.

Step-by-step explanation:

Rigid motion transformation : A transformation is called a rigid motion transformation if a point or object is moved, but the size and shape remain the same.

In rotation, the point of figure is rotated about the center of rotation but the size and shape remain the same.

Therefore rotation is a rigid transformation and option 1 is incorrect.

In dilation, the figure is stretched of compressed by the scale factor k along the center of dilation, so the size of figure is either increase of decrease.

Therefore dilation  is not a rigid transformation and option 2 is correct.

In translated, the point of figure is shifted but the size and shape remain the same.

Therefore translation is a rigid transformation and option 3 is incorrect.

In reflection, the point of figure is reflected about the line of reflection but the size and shape remain the same.

Therefore reflection is a rigid transformation and option 4 is incorrect.

one number that could round to 3 100 when rounded is 3 120

Answer:

its D

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

8.58 , 8.508 , 7.5 , 7.058 :]

Answer: 8.58, 8.508, 7.5, 7.058

Given

A rectangle is placed inside a circle whose diameter is 13unit all corners of it on the circle.

area of the rectangle = 60 square unit

Find the dimensions of the rectangle.

To proof

As given in the question

rectangle is placed inside a circle whose diameter is 13unit .

now by using the diagram given below

the diagonal of the rectangle is equal to the diameter of the circle.

Thus DB = 13 unit

FORMULA

Area of the rectangle = Length × Breadth

area of the rectangle =  60 square unit

let the value of the length be ( Say AB ) = x

put the value in the above equation

we get

60 = x  × Breadth

[tex]Breadth( say AD)= \frac{60}{x}[/tex]

now in ABD

Using the pythagorus theorem

we get

BD²= AB² + AD²

[tex]13^{2} = x^{2}+ (\frac{60}{x}) ^{2}[/tex]

solving the above equation

we get

[tex]169x^{2}= x^{4} + 3600[/tex]

[tex]x^{4} - 169x^{2}+3600 =0[/tex]  

[tex]x^{4} - 144x^{2} -25x^{2} + 3600 =0[/tex]

[tex]x^{2} (x^{2} - 144) - 25 (x^{2} - 144) =0[/tex]

(x² - 25) (x² -144) =0

The roots are

x = -12 ,-5, 5, 12

-12 and -5 are neglected  because of negative terms .

( Length and breadth of recangle cannot be negative )

thus x = 12 and 5

Two case arise

First case

when

Length of rectangle= 12unit

[tex]Breadth = \frac{60}{12}[/tex]

Breadth of rectangle = 5 unit

Second case

Length of rectangle= 5unit

[tex]Breadth = \frac{60}{5}[/tex]

Breadth of rectangle = 12 unit

Hence proved

Final answer:

To find the dimensions of a rectangle inside a circle with a diameter of 13, we use the Pythagorean Theorem and the area of the rectangle. After substituting values and solving, we find the dimensions are 5 units by 12 units.

Explanation:

To find the dimensions of the rectangle that fits inside a circle with a diameter of 13, one must first recognize that the rectangle forms the sides of a right-angled triangle where the diagonal of the rectangle serves as the hypotenuse of the triangle. This hypotenuse, thus, equals the diameter of the circle, which is 13 units.

Since the area of the rectangle is 60 square units, we let the sides of the rectangle be denoted as length (l) and width (w), with the area equation being l×w = 60.

Using the Pythagorean Theorem, we have: l2 + w2 = 132. We also know that lw = 60, which allows us to solve for one variable in terms of the other. Let's solve for w: w = 60/l. Substituting this into the Pythagorean equation gives l2 + (60/l)2 = 169. Solving this quadratic equation will give us the dimensions of the rectangle that can fit within the circle.

After solving, one finds that the dimensions that satisfy both the area and the Pythagorean Theorem are 5 and 12.

Therefore, the dimensions of the rectangle are 5 units by 12 units.

C. The square root of 3 is an irrational number. I hope that this helps!

Answer: (-3,4) and (9,20)

I think these two points will make the answer you have been looking for.

Answer:

about 105

Step-by-step explanation:

The degree of a complete rotation is 360 degrees.

5/6th of a rotation = 5/6 X 360

that is 300 degrees.

Thus the minute hand moves 300 degrees.

(Sorry, I'm not sure about the radians ;-) )

If the minute hand of a clock moves from 12 to 10 ​o'clock, or five-sixths of a complete revolution, by 300 degrees it​ will move.

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

It is given that, the minute hand of a clock moves from 12 to 10 ​o'clock, or five-sixths of a complete revolution.

The degree of a complete rotation is 360 degrees.

5/6th of a rotation it covers,

= 5/6 × 360

=300 degree

Any given angle must be multiplied by π/180 to be converted from the degree scale to the radian scale.

=300 × π/180

=5.235 radians

As a result 5.235 radians, will move.

Thus, if the minute hand of a clock moves from 12 to 10 ​o'clock, or five-sixths of a complete revolution, by 300 degrees it​ will move.

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 [tex]\sqrt{m^{4} n^{7} }[/tex]

= [tex]\sqrt{m*m*m*m*m*N*N*N*N*N*N*N}[/tex]

Look for groups of 2 (a group of two on the inside, makes one on the outside)

= [tex]m*m*N*N*N\sqrt{N}[/tex]

= [tex]m^{2} n^{3} \sqrt{n}[/tex]

Answer: C

[tex]x+7+14x[/tex]               Take off the parenthesis

[tex]15x+7[/tex]                    Combine Terms

*(Answer)*= [tex]15+7[/tex]

Hope this helps

BangtanBoyScouts

(1-52/2+5)=(1-26+5)=(-25+5)=-20

continuing:

-20*2*6*6= -40*6*6=-240*6=-1440

result: -1440

(2x)(x^2)+(2x)(x)+(2x)(-2)+(3)(x^2)+(3)(x)+(3)(-2)

Simplifying

(2x)(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Remove parenthesis around (2x)

2x(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Multiply x * x2

2x3 + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Remove parenthesis around (2x)

2x3 + 2x(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Multiply x * x

2x3 + 2x2 + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Remove parenthesis around (2x)

2x3 + 2x2 + 2x(-2) + (3)(x2) + (3)(x) + (3)(-2)

Reorder the terms for easier multiplication:

2x3 + 2x2 + 2 * -2x + (3)(x2) + (3)(x) + (3)(-2)

Multiply 2 * -2

2x3 + 2x2 + -4x + (3)(x2) + (3)(x) + (3)(-2)

Multiply 3 * -2

2x3 + 2x2 + -4x + 3x2 + 3x + -6

Reorder the terms:

-6 + -4x + 3x + 2x2 + 3x2 + 2x3

Combine like terms: -4x + 3x = -1x

-6 + -1x + 2x2 + 3x2 + 2x3

Combine like terms: 2x2 + 3x2 = 5x2

-6 + -1x + 5x2 + 2x3

Answer:

The product is,[tex]-6 + -1x + 5x2 + 2x3[/tex]

explanation:

Simplifying

[tex](2x)(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Remove the parentheses (2x)

[tex]2x(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Multiply [tex]x * x2[/tex]

[tex]2x3 + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Remove the closing parentheses (2x)

[tex]2x3 + 2x(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Multiply [tex]x * x[/tex]

[tex]2x3 + 2x2 + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Remove all parentheses (2x)

[tex]2x3 + 2x2 + 2x(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Rearrange the terms to make multiplication easier:

[tex]2x3 + 2x2 + 2 * -2x + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Multiply [tex]2 * -2[/tex]

[tex]2x3 + 2x2 + -4x + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Multiply [tex]3 * -2[/tex]

[tex]2x3 + 2x2 + -4x + 3x2 + 3x + -6[/tex]

Reorder the terms:

[tex]-6 + -4x + 3x + 2x2 + 3x2 + 2x3[/tex]

Combine like terms: -4x + 3x = -1x

[tex]-6 + -1x + 2x2 + 3x2 + 2x3[/tex]

Combine like terms: 2x2 + 3x2 = 5x2

[tex]-6 + -1x + 5x2 + 2x3[/tex]

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GameStop's total will be 371.00

Best Buy's total will be 337.90

Best Buy will be the better buy

Your answer is Best Buy

Answer:

The best option for buying the Xbox One is GameStop, as the final price would be of $315.35.

Step-by-step explanation:

GameStop: To obtain the price in GameStop, we must first obtain the 15% discount on the price of 350, and subtract it from the initial price. Then, we must calculate the amount of the tax and add it to the price to obtain the final price.

(350 - (350 x 0.15)) x 1.06 = $315.35

Best Buy: Instead, at Best Buy we simply add the sales price tax.

310 x 1.09 = $337.90

Using a system of equations based on the ratio of baskets made by Mr. McDonagh to Ms. Klein (13 to 2) and the information that Mr. McDonagh made 22 more baskets than Ms. Klein, we determine that Ms. Klein made 4 baskets and Mr. McDonagh made 26 baskets.

To solve how many baskets each person made, we will set up a ratio and use algebra to find the number of baskets made by Mr. McDonagh and Ms. Klein. We are given that for every 13 baskets Mr. McDonagh made, Ms. Klein made 2. Let's denote the number of baskets Mr. McDonagh made as M and the number of baskets Ms. Klein made as K.

According to the ratio, we can write [tex]\frac{M }{ K} = \frac{13 }{ 2}[/tex]. We also know that Mr. McDonagh made 22 more baskets than Ms. Klein, which can be written as M = K + 22. Now we have a system of equations:

[tex]\frac{M }{ K} = \frac{13 }{ 2}[/tex]

M = K + 22

Substitute M in the first equation with (K + 22):

[tex]\frac{K+22 }{ K} = \frac{13 }{ 2}[/tex]

2(K + 22) = 13K

2K + 44 = 13K

44 = 11K

Divide both sides by 11:

K = 4

Ms. Klein made 4 baskets. Now we can find how many baskets Mr. McDonagh made by substituting K back into one of our original equations:

M = 4 + 22

M = 26

Mr. McDonagh made 26 baskets.

Answer:

12

Step-by-step explanation:

2 times 2 is 4

4 divided by 2 is 2

2 times 2 is 4

2 times 6 is 12

12 divided by 2 is 6

4 plus 2 plus 6 is 12