Find the interquartile range for a data set having the five-number summary: 5.6, 11.1, 19.2, 24.5, 33.3

A. 13.6
B. 27.7
C. 13.4
D. 14.1

The property of real numbers that justifies the work done to simplify the expressions below is the distributive property of multiplication.

The distributive property of multiplication states that the same result is obtained by multiplying the sum of two or more addends by a number or multiplying each addend individually and adding the products.

The steps for the distributive property of multiplication are:

Thus, the property of real numbers that justifies the work done to simplify the expressions below is the distributive property of multiplication.

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Answer:

55 degrees

Step-by-step explanation:

Hi there!

The sum of the interior angles of a triangle is always 180 degrees.

We can solve for the interior angles at the bottom by subtracting both 135 and 100 from 180 (because straight lines have a measure of 180 degrees too):

180-135 = 45 degrees

180-100 = 80 degrees

Now, to solve for the final angle at the top, subtract 80 and 45 degrees from 180:

180-80-45 = 55 degrees

This angle at the top measuring 55 degrees is the opposite angle of x. Opposite angles are always congruent, so therefore, x measures 55 degrees.

I hope this helps!

Answer:

Line 1: (9+x)x

Line 2: x(9 + x)

The order of multiplies changed.

This is called a Commutative Property of Multiplication.

Line 3: x(x+9)

The order of added terms within parenthesis changed.

This is called a Commutative Property of Addition.

Line-1 to Line 2- Commutative property of multiplication

Line-2 to Line-3 =Commutative property of addition

Lets solve

[tex]\\ \rm\longmapsto (9+x)x[/tex]

[tex]\\ \rm\longmapsto x(9+x)[/tex]

[tex]\\ \rm\longmapsto x(x+9)[/tex]

[tex]\\ \rm\longmapsto x^2+9x[/tex]

Answer:

314ft²

Step-by-step explanation:

A = 3.14(10²)

A = 3.14 x 100

A = 314ft²

Answer:

Area is 314 ft²

Step-by-step explanation:

[tex]A = \pi {r}^{2} [/tex]

r is radius,

[tex]r = \frac{diameter}{2} = \frac{20}{2} = 10 \: ft[/tex]

therefore:

[tex]A = 3.14 \times {10}^{2} \\ A = 3.14 \times 100 \\ A = 314 \: {ft}^{2} [/tex]

Step-by-step explanation:

we first find the gradient

when y1=-4, x1=-5 and y2=1, x2=4

gradient={(y2-y1)÷(x2-x1)}

gradient={1-(-4)}÷{4-(-5)}

gradient=(1+4)÷(4+5)

gradient=5÷9 OR 0.5555

To find the equation interm of x

we substitute for the gradient in the formula

y-y1=gradient (x-x1)

y-(-4)=(5÷9)(x-×-5)

y+4=(5÷9)(x+5)

y+4=(5x+25)÷9 Cross multiply ✖️

9(y+4)=(5x+25)(1)

9y+36=5x+25 collect like terms

9y=5x+25-36

9y=5x-11 divide both sides by 9

y=(5x-11)÷9.......ans

Answer:

SP=Rs.700

Step-by-step explanation:

cost price of a copy=R's.25

cost price of 20copy=20×25=Rs.500

profit=Rs.200

selling price of 20 copies=?

Now, we know that,

profit=sp-cp

or, 200=sp-500

or, 200+500=sp

thus, SP=Rs.700

Hence, the selling price of 20copies is 700.

Answer:

Range is 19.54

Step-by-step explanation:

I. If R = H - L

when R is Range, H is highest value and L is lowest value

R = 25.6 - 6.06

R = 19.54

(a) From the histogram, you can see that there are 2 students with scores between 50 and 60; 3 between 60 and 70; 7 between 70 and 80; 9 between 80 and 90; and 1 between 90 and 100. So there are a total of 2 + 3 + 7 + 9 + 1 = 22 students.

(b) This is entirely up to whoever constructed the histogram to begin with... It's ambiguous as to which of the groups contains students with a score of exactly 60 - are they placed in the 50-60 group, or in the 60-70 group?

On the other hand, if a student gets a score of 100, then they would certainly be put in the 90-100 group. So for the sake of consistency, you should probably assume that the groups are assigned as follows:

50 ≤ score ≤ 60   ==>   50-60

60 < score ≤ 70   ==>   60-70

70 < score ≤ 80   ==>   70-80

80 < score ≤ 90   ==>   80-90

90 < score ≤ 100   ==>   90-100

Then a student who scored a 60 should be added to the 50-60 category.

Answer:

2b - 14

Step-by-step explanation:

2(b – 7)

2b - 14

Answer:

[tex]2b-14[/tex]

Step-by-step explanation:

Using the distributive property, [tex]2(b-7)[/tex] can be written as [tex](2\cdot b)-(2\cdot7)[/tex] which solved/simplified is [tex]2b-14[/tex]

Man, it's late! Well, hope this helped you out and answered your question!

Answer:

volume of a cylinder

V= TTr² h

V= volume

TT= pie

h= height

Step-by-step explanation:

Note: radius is 2times diameter ... if you are given diameter and to convert to radius, divide the diameter by 2

V=TTr²h

r= 8/2 =4cm

V= 3×4²×12

V=3×16×12=576cm³

Answer:

4 miles per hour

Step-by-step explanation:

hi <3

product means multiplication, therefore we know there has to be a '2k' and we can eliminate option A

also, there is a mention of subtraction, so we can also eliminate option B

now we are left with C and D

it is stated that it is being subtracted FROM 17, therefore the 17 would have to come first

in short, your answer is option C

hope this helps :)

The product of 2 and a number k, subtracted from 17 is the expression: c. 17-2k.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

given that,

The product of 2 and a number k, subtracted from 17

we have to find the expression for given statement.

let the number be x

now, we have,

The product of 2 and a number k,

i.e. 2*k = 2k

then,  subtracted from 17

i.e. 17 - 2k

so, we get,

x = 17 - 2k

Hence, The product of 2 and a number k, subtracted from 17 is the expression: c. 17-2k.

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Answer:

option b is the correct answer.

Explanation is beloe

Step-by-step explanation:

x²+y²=9

xy=8

x+y=?

Now,

(x+y)²=x²+2×x×y+y²

(x+y)²=x²+2xy+y²

(x+y)²=x²+y²+2xy

(x+y)²=9+2×8

(x+y)²=9+16

(x+y)²=25

(x+y)²=5²

x+y=±5

I hope it helped U

stay safe stay happy

Step-by-step explanation:

[tex]we \: have \: {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ here \: {x}^{2} + {y}^{2} = 9 \\ xy = 8 \\ then {(x + y)}^{2} = 9 + 2 \times 8 \\ {(x + y)}^{2} = 9 + 16 = 25 \\ {(x + y)}^{2} = 25 \\ x + y = \sqrt{25} = +/-5 \\ thank \: you[/tex]

Answer:

.75

Step-by-step explanation:

8 red marbles, 3 blue marbles, and 1 green marble = 12 marbles

P( not blue) = marbles that are not blue / total

                     =(8red+1 green) / 12

                     =9/12

                      = 3/4

                       .75

Answer:

123 456lcm divison method

Answer:

four hundred and thirty two million, five hundred and fifty three thousand, six hundred and two

Step-by-step explanation:

Answer:

Four hundred thirty-two million, five hundred fifty-three thousand, six hundred and two.

Step-by-step explanation:

Answer:

4y-5x-44=0

Step-by-step explanation:

It passes through one point with the formula being

y-y1=m(x-x1)

y-6=5/4(x-(-4))

y-6=5/4(x+4)

cross multiply

4(y-6)=5(x+4)

4y-24=5x+20

collect like terms

4y-5x=20+24

4y-5x=44

4y-5x-44=0

Answer:

Step-by-step explanation:

I will ASSUME you want an equation

In slope/intercept form it is

6 = (5/4)(-4) + b

b = 11

y = (5/4)x + 11

or in slope/point form is

(y - 6) = (5/4)(x + 4)

Step-by-step explanation:

here ,

the total cost of copy is rs 5 and 3 upin 4 =5.75

the total cost of book is rs 15 and 5 upon 6 =12.5

so the cost of book is more then copy by 6.75(12.5-5.75)

Answer:

8

Step-by-step explanation:

4/3 cup for 3 dozen.

how many cups for 18 dozen ?

what factor do I need to use to turn 3 into 18 ?

3×x = 18

x = 18/3 = 6

so, I need 6 units of flour (1 unit is 4/3 cup) to make 6 units of cookies (1 unit is 3 dozen).

therefore, we need

4/3 × 6 = 6×4/3 = 2×4 = 8 cups of flour.

Answer:

7-15= -8

Step-by-step explanation:

Answer:

Ab paralelo DC

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

1.2*10 = 1.2

Answer:

12

Step-by-step explanation:

the "normal form" to write numbers : just the digits and a decimal point when needed.

so, 1.2 × 10 = 12

12 is the normal, standard decimal notation.

in some cases it can be also 12.0 or 12.00 (especially with money).

the other form is the scientific notation, where a number is written with its leading digits and the power of 10 as the total value "weight". like in this example 1.2 × 10¹

Answer:

Step-by-step explanation:

The key features of a quadratic function are the y-intercept, the axis of symmetry, and the coordinates and nature of the turning point (or vertex)

for opposite: Its reflection and its symmetrical

opposite function or inverse functions are reflections of each other over the line y = x. You find the inverse by switching x and y in the equation.

Answer:

[tex]\displaystyle \text{min} = \frac{\sqrt{3+2\sqrt{3}}}{2} - \frac{2\sqrt[4]{3}}{\sqrt{2}} \text{ at } x = \frac{\sqrt{3}}{2}\text{ and } \\ \\ \text{max} = 2\sqrt{5} -4 \text{ at } x = 4[/tex]

Step-by-step explanation:

We want to find the maximum and minimum values of the function:

[tex]\displaystyle f(x) = \sqrt{x + x^2} - 2\sqrt{x}[/tex]

On the interval [0, 4].

First, evaluate its endpoints:

[tex]\displaystyle \begin{aligned} f(0) &= \sqrt{(0)+(0)^2} - 2\sqrt{0} \\ &= 0 \\ \\ f(4) &= \sqrt{(4)+(4)^2} - 2\sqrt{(4)} \\ &= 2\sqrt{5} -4 \end{aligned}[/tex]

Recall that the extrema of a function occurs at its critical points; that is, where its derivative equals zero (or is undefined).

Take the derivative of both sides:

[tex]\displaystyle f'(x) = \frac{d}{dx}\left[ \sqrt{x + x^2} - 2\sqrt{x}\right][/tex]

Differentiate:

[tex]\displaystyle \begin{aligned} f'(x) &= \frac{1}{2\sqrt{x + x^2}} \cdot (1 + 2x) - 2\left(\frac{1}{2\sqrt{x}}\right) \\ \\ &= \frac{2x+1}{2\sqrt{x+x^2}} - \frac{1}{\sqrt{x}} \\ \\\end{aligned}[/tex]

Note that the derivative is undefined at x = 0. Hence, x = 0 is a critical point.

Solve for the zeros of the derivative:

[tex]\displaystyle\begin{aligned} \frac{2x+1}{2\sqrt{x + x^2}} - \frac{1}{\sqrt{x}} &= 0\\ \\ \frac{2x+1}{2\sqrt{x}\sqrt{1 + x }} - \frac{1}{\sqrt{x}} &= 0 \\ \\ \frac{2x+1}{2\sqrt{1+x}} - 1 &= 0\\ \\ 2x + 1 &= 2\sqrt{1+x} \\ \\ 4x^2 + 4x + 1 &= 4 + 4x \\ \\ x^2 &= \frac{3}{4} \\ \\ x= \frac{\sqrt{3}}{2} \end{aligned}[/tex]

Therefore, our only two critical points are at x = 0 and x = √3/2:

Evaluate the function at x = √3/2:

[tex]\displaystyle \begin{aligned} f\left(\frac{\sqrt{3}}{2}\right) &= \sqrt{\left(\frac{\sqrt{3}}{2} \right)+ \left(\frac{\sqrt{3}}{2}\right)^2} - 2 \sqrt{\left(\frac{\sqrt{3}}{2}\right)} \\ \\ &= \frac{\sqrt{3+2\sqrt{3}}}{2}- \frac{2\sqrt[4]{3}}{\sqrt{2}} \\ \\ &\approx -0.5900\end{aligned}[/tex]

In conclusion: the exact maximum and minimum values of f on the interval [0, 4] is:

[tex]\displaystyle \text{min} = \frac{\sqrt{3+2\sqrt{3}}}{2} - \frac{2\sqrt[4]{3}}{\sqrt{2}} \text{ at } x = \frac{\sqrt{3}}{2}\text{ and } \\ \\ \text{max} = 2\sqrt{5} -4 \text{ at } x = 4[/tex]

Answer:

V=880

Step-by-step explanation:

V=π(R^2 − r^2)L

V=(22/7)*7*(11^2-9^2)

V=880

Answer:

yes

Step-by-step explanation:

x - 4y = 15

Substitute the point into the equation and see if the equation is true

7 -4(-2) = 15

7+8 = 15

15 =15

This is true so the point is a solution to the equation

Answer:

it's D

Step-by-step explanation:

2 dozen is 24 so we have 18 pnt butter and 24 choc chip.

they're putting 4 choc chp in each so do 24/4

they're putting 3 pnt butter in each so do 18/3

both are 6 so D is the answer

Answer:

$3480

Step-by-step explanation:

We know that the tax rate for the first $8000 is 15% and after $8000 the tax is 19%.

This means the total amount of money that Christine have to pay is equal to $8000 × 15% + ($20000 (the total) - $8000 (the amount that she already paid for the first $8000)) × 19%

This is equal to $1200 + $12000 × 19%

= $1200 + $2280

= $3480

Therefore, Christine must pay $3480 in income tax.