what is the interquartile range of 2 5 9 11 18 30 42 55 58 73 81

Answer:

1. [tex]1. (\frac{5}{16}) (-2) (-4) (\frac{-4}{5})= -2 \\2. (2\dfrac{3}{5}) (\frac{7}{9})=(\frac{91}{45})\\3. (\frac{2}{3})(-4)(9)= -24\\4. (\frac{-3}{4}) (\frac{7}{8})=(\frac{-21}{32})[/tex]

Step-by-step explanation:

These are simple multiplication questions of fractions. We multiply numerator with numerators and denominators with denominators. If numerator and denominator is both divisible by same number we can divide them for simplification.

1. [tex](\frac{5}{16}) (-2) (-4) (\frac{-4}{5})[/tex]

[tex]=(\frac{-10}{16}) (-4) (\frac{-4}{5})\\=(\frac{40}{16}) (\frac{-4}{5})\\=(\frac{-160}{80}) \\dividing\,\, numerator\,\, and\,\, denominator\,\, by\,\, 80\,\,\\= -2[/tex]

2. [tex](2\dfrac{3}{5}) (\frac{7}{9})[/tex]

Converting mixed form into fraction form,

[tex]=(\frac{13}{5})(\frac{7}{9})[/tex]

Multiplying numerators with each other and denominators with each other

[tex]=(\frac{13*7}{5*9})\\=(\frac{91}{45})[/tex]

3. [tex](\frac{2}{3})(-4)(9)[/tex]

Multiplying these terms with each other:

[tex]=(\frac{2*-4}{3})(9)\\=(\frac{-8}{3})(9)\\=(\frac{-8*9}{3})\\=(\frac{-72}{3})\\[/tex]

Dividing numerator and denominator with 3

[tex]=-24[/tex] 

[tex]4. (\frac{-3}{4}) (\frac{7}{8})\\=(\frac{-3}{4}) (\frac{7}{8})\\=(\frac{-3*7}{4*8})\\=(\frac{-21}{32})[/tex]

Hi, hope this helps you out. I understand how this can be confusing. Have a great day! :)

Answer:

[tex]\frac{10y - 11}{(y - 1)(y - 2)( y + 1)}[/tex]

Step-by-step explanation:

1. Factor [tex]y^2 - 3y + 2[/tex]:

How-to:

After breaking the expression into groups, you're left with [tex](y^2 - y) + (-2y + 2)[/tex]. Factor out y from [tex]y^2 - y[/tex][tex]: y(y - 1)[/tex]. Factor out [tex]-2[/tex] from [tex]-2y + 2: -2(y - 1)[/tex]  = [tex]y( y - 1) - 2(y - 1)[/tex].  Finally, factor out common terms (in your case, y -1 ) and you're left with: [tex](y - 1)(y - 2)[/tex] Now you have [tex]\frac{3}{(y - 1)(y - 2)} + \frac{7}{y^2 - 1}[/tex]

2. Find the least common multiple of [tex]( y - 1)(y - 2), (y + 1)(y - 1)[/tex].

How-to:

Find an expression comprised of factors that appear in [tex]( y - 1)(y - 2), (y + 1)(y - 1)[/tex]. You'll find [tex](y - 1)(y - 2)(y + 1)[/tex]. Adjust your fractions based on the LCM and you'll get [tex]\frac{3(y + 1)}{(y - 1)(y - 2)(y + 1)}  + \frac{7 (y - 2)}{(y + 1)(y - 1)(y - 2)}[/tex]

3. Since the denominators are equal, combine the fractions above. You'll get [tex]\frac{3(y + 1) + 7(y - 2)}{(y - 1)(y - 2)(y + 1)}[/tex]

4. Expand [tex]\frac{3(y + 1) + 7(y - 2)[/tex] and you'll get [tex]10y - 11[/tex]. This is your new numerator.

Finally, your simplified operation is: [tex]\frac{10y - 11}{(y - 1)(y - 2)( y + 1)}[/tex]

To simplify an operation in mathematics, follow these steps: combine like terms, perform arithmetic operations, simplify fractions, and express the result in a simplified form.

When simplifying an operation in mathematics, you want to reduce the expression or equation to its simplest form. This may involve combining like terms, performing any necessary arithmetic operations, or simplifying fractions. Here are the steps to simplify an operation:

By following these steps, you can simplify any mathematical operation.

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Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}m+n=5&\text{subtract}\ n\ \text{from both sides}\\5m+5n=25\end{array}\right\\\\\left\{\begin{array}{ccc}m=5-n&(1)\\5m+5n=25&(2)\end{array}\right\qquad\text{put (1) to (2):}\\\\5(5-n)+5n=25\qquad\text{use the distributive property}\\\\(5)(5)+(5)(-n)+5n=25\\\\25-5n+5n=25\qquad\text{cancel}\ 5n\\\\25=25\qquad\bold{TRUE}[/tex]

Answer:

x¹⁰y¹⁵

Step-by-step explanation:

Expression: (x²y³)⁵

When a number to a power is multiplied by another power, then the exponents are multiplied. e.g. (a⁴)⁶ = a²⁴

So here, for x, the exponent is 2 * 5 = 10, and for y, it is 3 * 5 = 15.

So that gives us (x²y³)⁵ = x¹⁰y¹⁵

Answer:

A

Step-by-step explanation:

Answer:

Option A, By investing in goods and services

, is the right answer.

Step-by-step explanation:

Option A, investing in goods and services is the correct answer because the investment on goods and services will generate employment in the country and person will be able to earn more and consequently the expenditure will also increase. Moreover, if there will be more production of goods and services then the country’s GDP and economy will boost.

Answer:

the 23.7 ounce bottle is the better price because the 14.2 ounce bottle is $0.35 and the 23.7 ounce bottle is $0.29.

Step-by-step explanation:

you simply divide the cost by the ounces and get the unit price

To find the unit price for each size, divide the cost of the shampoo by the number of ounces. The 23.7-ounce bottle is the better buy based on the lower unit price.

To find the unit price for each size, divide the cost of the shampoo by the number of ounces in each bottle. For the 14.2-ounce bottle, the unit price is $0.35 per ounce ($4.98 / 14.2). For the 23.7-ounce bottle, the unit price is $0.29 per ounce ($6.97 / 23.7).

To determine which size is the better buy based on the unit price, compare the unit prices. Since the 23.7-ounce bottle has a lower unit price ($0.29 per ounce) compared to the 14.2-ounce bottle ($0.35 per ounce), the larger size is the better buy.

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Answer:

Step-by-step explanation:

Answer:

96

Step-by-step explanation:

a^2 + 8^2 = 10^2

a^2 = 36

a = 6

6 * 16 = 96

Answer:

[tex]y=2\sin (x-\pi)[/tex]

Step-by-step explanation:

The sine graph has an amplitude of 2.

The period of this function is [tex]2\pi[/tex]

The graph is obtained by shift the graph of [tex]y=\sin x[/tex] [tex]\pi[/tex] units to the right.

Among the given equations, the only function which has these properties is

[tex]y=2\sin (x-\pi)[/tex]

The correct answer is option A

Answer:

D.) 42 cubes

Step-by-step explanation:

Instead of counting each cube, you can find the volume.

The formula to find volume is ( Volume = Length x Width x Height)

                                                  ( V= 2 x 7 x 3)

2 x 7 x 3 = 42 cubes

I hope this helped you ; )

Answer:

21

Step-by-step explanation:

Let's use the point-slope formula...

y-y1=m(x-x1)

m is the slope.

y--9=7(x--2)

Subtracting a negative number is the same as adding a positive number...

y+9=7(x+2)

y+9=7x+14

Let's subtract 9 from both sides...

-9+y+9=7x+14-9

y=7x+5

The formula is now in the format of...

y=mx+b

This is known as slope-intercept.

m is the slope.

b is the y-intercept, the value of y when x=0.

Standard formula is...

Ax+By=C

Neither A nor B equal zero.

A is greater than zero.

y=7x+5

Let's move 7x to the left side of the equation.  It becomes negative.

-7x+y=5

Let's multiply both sides by -1 to render A greater than zero.

-1(-7x+y)=(5)(-1)

7x-y=-5

This is the equation in standard form.

[tex]

\text{d stands for distance between two points} \\

d(A, B)=\sqrt{(\Delta{x})^2+(\Delta{y})^2} \\

\text{or simply} \\

d(A, B)=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\

\text{now put in the data} \\

d(A, B)=\sqrt{(-2-15)^2+(9-9)^2} \\

d(A, B)=\sqrt{(-17)^2} \\

d(A, B)=\boxed{17} \\

[/tex]

Answer:

15/2 in³

Step-by-step explanation:

The formula for the vol. of a pyramid

is

V = (1/3)(area of base)(height of pyramid)

Here, the volume is:

V = (1/3)( [1/2][5 in][9 in] )·(10 in)

   = (9/3)(5/2)(10) in³

    =  450/6 in³   =   150/2 in³  =  75 in³     Volume of the pyramid

Answer:

Step-by-step explanation:

The formula of a volume of a pyramid:

[tex]V=\dfrac{1}{3}BH[/tex]

B - area of a base

H - height

In a base we have the right triangle with legs 9in and 5in.

The formula of an area of a right triangle:

[tex]A=\dfrac{ab}{2}[/tex]

ab - legs

Substitute:

[tex]B=\dfrac{(5)(9)}{2}=\dfrac{45}{2}\ in^2[/tex]

The height H = 10 in.

Calculate the volume:

[tex]V=\dfrac{1}{3\!\!\!\!\diagup_1}\left(\dfrac{45\!\!\!\!\!\diagup^{15}}{2\!\!\!\!\diagup_1}\right)(10\!\!\!\!\!\diagup^5)=(1)(15)(5)=75\ in^3[/tex]

Answer:

[tex]5.5\ years[/tex]

Step-by-step explanation:

we know that

In this problem we have a exponential function of the form

[tex]f(x)=a(b^{x})[/tex]

where

x is the time in years

f(x) is the value of the stock

a is the initial value

b is the base

r is the rate

b=(1-r)

we have

[tex]a=\$15,000[/tex]

[tex]r=4\%=4/100=0.04[/tex]

[tex]b=(1-0.04)=0.96[/tex]

substitute

[tex]f(x)=15,000(0.96^{x})[/tex]

80% of original price is equal to

[tex]f(x)=0.80(15,000)=12,000[/tex]

so

For f(x)=12,000 ------> Find the value of x

[tex]12,000=15,000(0.96^{x})[/tex]

[tex](12/15)=(0.96^{x})[/tex]

Apply log both sides

[tex]log(12/15)=log(0.96^{x})[/tex]

[tex]log(12/15)=(x)log(0.96)[/tex]

[tex]x=log(12/15)/log(0.96)[/tex]

[tex]x=5.5\ years[/tex]

Answer:

B. I belive ^_^

Step-by-step explanation:

Answer:

The third answer choice.

Step-by-step explanation:

If a function has more than one ordered pairs with the same x value (in this case it is x= 4), then it cannot be a function :)

This problem involves the uses of the Pythagorean Theorem as well as the use of Sine.

To start we need to identify what we know and what we don't know. We know that there are two triangles. We are given 2 sides lengths and an angle in one and only an angle in the other. They share one side meaning when we are given 2 sides in one triangle it will be easy to get the third side. What we don't know is the side length of CB DB or CD. We need to find CB in order to find CD.

Pythagorean Theorem for side length CB:

12^2-6^2=√108

√108=10.4 (average)

So CB is equal to 10.4

Sine Calculation for side length CD:

Since we have angle 56* we will use the length we found which will be the opposite side from the angle and then input x for our hypotenuse CD in order to solve.

sin 56* = 10.4/x

sin 56* × x = 10.4/x × x

sin 56*x = 10.4

/sin 56*      /sin 56*

x = 12.544....

or 12.6 (average)

So, to conclude, our answer for CD is 12.6cm.

Hope I helped!

Answer:

12.7 cm

Step-by-step explanation:

Given information: AB=6cm AC=12cm.

Pythagoras theorem: In a right angle triangle

[tex]hypotenuse^2=base^2+perpendicular^2[/tex]

Using Pythagoras in triangle ABC we get

[tex](AC)^2=(AB)^2+(BC)^2[/tex]

[tex](12)^2=(6)^2+(BC)^2[/tex]

[tex]144-36=(BC)^2[/tex]

[tex]108=(BC)^2[/tex]

Taking square root on both sides.

[tex]\sqrt{108}=BC[/tex]

Law of sine:

[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

Using law of sin we get

[tex]\dfrac{CD}{\sin (90)}=\dfrac{\sqrt{108}}{\sin (55)}[/tex]

[tex]\dfrac{CD}{1}=\dfrac{\sqrt{108}}{\sin (55)}[/tex]         [tex][\because \sin 90^{\circ}=1][/tex]

[tex]CD=12.6866616739[/tex]

Approx the data to three significant figures.

[tex]CD\approx 12.7[/tex]

Therefore, the length of CD is 12.7 cm.

Answer:

392

Step-by-step explanation:

Squares get really big very quickly, so you don't want to use any bigger numbers. The biggest total of the squares would be from

using

1 and 28

1+28

2=1+784=785

2 and 27=4+729=733

142+14

2=196+196=392

The greater the difference between the two numbers, the bigger one of the numbers is going to be.

Therefore use two numbers with the smallest difference between them which will be

14 and 14

The minimum value of sum of their square is 392.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Let the Bigger no. = x

Let the Smaller no. = y

x - y = 28 (given)

(x - y)^2 = 28^2

x^2 + y^2 - 2xy = 784

x^2 + y^2 = 784 + 2xy

Let the value of x = 14 and y = -14 (By trial and error)

Hence, the minimum value of sum of squares will be 14^2 + 14^2 = 392.

Learn more about equations on:

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For this case we have the following equation:

[tex]39.7 + b + 30.1 = 165.288[/tex]

We must find the value of the variable "b":

We follow the steps below:

We add similar terms:

[tex]39.7 + 30.1 + b = 165.288\\69.8 + b = 165.288[/tex]

We subtract 69.8 on both sides of the equation:

[tex]b = 165.288-69.8\\b = 95,488[/tex]

Thus, the value of b is 95,488

Answer:

[tex]b = 95,488[/tex]

There is a 46% chance of a female patient having type-O blood

Answer:

19.6

Step-by-step explanation:

The question is slightly ambiguous. The data tells us that the number of females with O blood is 140.

I think you take this out of the entire population which is 714

The % is (140 / 714)   *  100 = 19.61%

I wouldn't bet on these numbers being accurate.

Answer:

Step-by-step explanation:

The only solution is x=2

5(2x-3)=5

Divide each term by 5 and simplify

2x−3=12x-3=1

Move all terms not containing x

to the right side of the equation.

2x=42x=4

Divide each term by 2

x=2

Answer:

The given solution has only one solution which is x=2

Step-by-step explanation:

Given the equation

[tex]5(2x-3)=5[/tex]

we have to find the solution of above equation.

Equation is

[tex]5(2x-3)=5[/tex]

Divide by 5 throughout the equation

[tex]2x-3=\frac{5}{5}=1[/tex]

[tex]2x-3=1[/tex]

Adding 3 on both sides

[tex]2x=4[/tex]

Dividing throughout by 2, we get

[tex]x=\frac{4}{2}=2[/tex]

Hence, the given solution has only one solution which is x=2

Answer:

The answer is going to be D) . 14

Step-by-step explanation:

Hello!

Answer:

D

Step-by-step explanation:

7.2.11 = 11.t

14.11 = 11.t

154 = 11.t

14 = t

Answer:

cos13°

Step-by-step explanation:

Using the cofunction identity

sinx° = cos(90 - x)°

sin77° = cos(90 - 77)° = cos13°

Answer:(5/4,0)

Step-by-step explanation:

The process of rounding 895,472 to the nearest 100,000 involves examining the ten thousands place of the number. Given it's 9, the number is rounded up to 900,000.

The question is asking to round the number 895,472 to the nearest 100,000. To do this, you should look at the ten thousands place of the number, which is 9. If this digit is 5 or greater, round the hundreds of thousands place up. If it is less than 5, round down. In this case, since the ten thousands place is 9, we round 800,000 up to 900,000. Therefore, 895,472 rounded to the nearest 100,000 is 900,000.

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Answer:

[tex]\frac{\sqrt{5} }{x^{2} y}[/tex]

Step-by-step explanation:

That's a complex expression, let's simplify it, step by step, off the start, we'll simplify the 55/11:

[tex]\sqrt{ \frac{55 x^{7} y^{6} }{11 x^{11} y^{8} } } = \sqrt{ \frac{5 x^{7} y^{6} }{x^{11} y^{8} } }[/tex]

Then we'll simplify the x's and y's:

[tex]\sqrt{ \frac{5 x^{7} y^{6} }{x^{11} y^{8} } } = \sqrt{ \frac{5}{x^{4} y^{2} } }[/tex]

Let's split the square root in two and solve the bottom part:

[tex]\sqrt{ \frac{5}{x^{4} y^{2} } } = \frac{\sqrt{5} }{\sqrt{x^{4} y^{2}} } = \frac{\sqrt{5} }{x^{2} y}[/tex]

The solution is then:

[tex]\frac{\sqrt{5} }{x^{2} y}[/tex]

The expression which is equivalent to the given expression is:

          [tex]\dfrac{\sqrt{5}}{x^2y}[/tex]

We are given a expression as:

     [tex]\sqrt{\dfrac{55x^7y^6}{11x^{11}y^8}}[/tex]

Now we know that:

[tex]55=11\times 5[/tex]

Hence, we get:

 [tex]\sqrt{\dfrac{55x^7y^6}{11x^{11}y^8}}=\sqrt{\dfrac{11\times 5x^7y^6}{11x^{11}y^8}[/tex]

which is written as:

[tex]\sqrt{\dfrac{5x^7y^6}{x^{11}y^8}}[/tex]

Also, we know that if n>m

Then

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

Hence, we have the expression as:

[tex]=\sqrt{\dfrac{5}{x^{11-7}y^{8-6}}}\\\\\\=\sqrt{\dfrac{5}{x^4y^2}[/tex]

This could be given as:

[tex]=\dfrac{\sqrt{5}}{\sqrt{x^4}\sqrt{y^2}}[/tex]

Now, we know that:

[tex]\sqrt{x^4}=\sqrt{(x^2)^2}=x^2\\\\and\\\\\sqrt{y^2}=y[/tex]

Hence, we get that:

[tex]\sqrt{\dfrac{55x^7y^6}{11x^{11}y^8}}=\dfrac{\sqrt{5}}{x^2y}[/tex]

Answer: First consider the case that ‘just’ 5 persons are seated around a round table.

Clearly, ‘just’ 5 persons can be seated around a round table in (5 - 1)! = 4! = 24 ways.

Now, one vacant chair is to be inserted among them.

Say, for a particular sitting arrangement ‘ABCDE’; there are 5 scopes available for inserting the vacant chair - between A and B, between B and C, between C and D, between D and E & between E and A.

So, there are 5*24 = 120 ways available that 5 persons can sit around a round table with 6 chairs.

Step-by-step explanation:

First consider the case that ‘just’ 5 persons are seated around a round table.

Clearly, ‘just’ 5 persons can be seated around a round table in (5 - 1)! = 4! = 24 ways.

Now, one vacant chair is to be inserted among them.

Say, for a particular sitting arrangement ‘ABCDE’; there are 5 scopes available for inserting the vacant chair - between A and B, between B and C, between C and D, between D and E & between E and A.

So, there are 5*24 = 120 ways available that 5 persons can sit around a round table with 6 chairs.

[tex]x2y + z = 9 \\ \\ 1. \: x + 2y + z + - 2y = 9 + - 2y \\ x + z = - 2y + 9 \\ 2. \: x + z + - z = - 2y + 9 + - z \\ x = - 2y - z + 9 \\ \\ \\ x + y - z = 5 \\ \\ 1. \: x + y - z + - y = 5 + - y \\ x - z = - y + 5 \\ 2. \: x - z + z = - y + 5 + z \\ x = - y + z + 5 \\ \\ \\ 3x - y + 2z = 12 \\ 1. \: 3x - y + 2z + y = 12 + y \\ 3x + 2z = y + 12 \\ 2. \: 3x = y - 2z + 12 \\ 3. \: \frac{3x}{3} = \frac{y - 2z + 12}{3} \\ x = \frac{1}{3} y + \frac{ - 2}{3} z + 4[/tex]

===================================================

Explanation:

The idea is that for any term, we add on the common difference d to get the next term. For example, the sequence {3, 7, 11, 15, 19, 23, ...} has us add on 4 each time so d = 4 in this case.

3+4 = 7

7+4 = 11

11+4 = 15

and so on. The nth term is represented by the notation[tex]a_n[/tex] while the term just before the nth term is written as [tex]a_{n-1}[/tex]

So adding d onto the term just before the nth term gets us the nth term which is how we end up with [tex]a_n = a_{n-1}+d[/tex]

This is the recursive form of the arithmetic sequence. The closed form is written as [tex]a_n = a_1 + d(n-1)[/tex]

Answer:

1 x 1,000,000 + 9 x 100,000 + 4 x 10,000 + 8 x 1,000 + 4 x 100 + 4 x 10 + 7 x 1

Hope I helped : )

Step-by-step explanation:

The place value chart can help us to write a number in expanded notation.

When we put 1,948,447 into the place value chart, we can recognize that our number is equal to 1 million + 9 hundred thousands + 4 ten thousands + 8 thousands + 4 hundreds + 4 tens + 7 units.

Answer:

140 inches

Step-by-step explanation:

You do the base(14) times the hieght(10)

14x10=140

Answer: [tex]x=\frac{89}{3}[/tex], or [tex]29\frac{2}{3}[/tex]

[tex]\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\6x+2-2=180-2\\6x=178[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}6\\\frac{6x}{6}=\frac{178}{6}\\[/tex]

[tex]x=\frac{89}{3}[/tex]

Hope this helps and have a great day!!!

Answer:

x = 29 2/3

Step-by-step explanation:

6x + 2 = 180

6x = 180 - 2

6x = 178

x = 178 ÷ 6

x = 89/3

x = 29 2/3