2/5 m = ____ cm



5/6 year = _____ months


ONLY IN FRACTION

The value of the given expression is 5^(3/4).

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression can be resolved as shown below,

5² ÷ √5

[tex]= \dfrac{5^2}{\sqrt5}\\\\\\[/tex]

Using the law of exponents, [tex]\sqrt[n]{m} = m^{\frac1n}[/tex],

[tex]= \dfrac{5^2}{5^{\frac12}}\\\\\\[/tex]

Using the law of exponents, [tex]m^x\times m^y = m^{x+y}[/tex],

[tex]= {5^2} \times {5^{-\frac12}}[/tex]

Solving the powers,

[tex]= {5^{2-\frac12}}\\\\= 5^{\frac34}[/tex]

Hence, the value of the given expression is 5^(3/4).

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The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same ratetion:

Answer:

The derivative is:

[tex]f^{\prime}(x) = -\frac{5}{x^2-6x+9}[/tex]

Step-by-step explanation:

We are given the following function:

[tex]f(x) = \frac{5}{3-x}[/tex]

Derivative of a quotient:

Suppose we have a quotient:

[tex]f(x) = \frac{g(x)}{h(x)}[/tex]

The derivative is:

[tex]f^{\prime}(x) = \frac{g^{\prime}(x)h(x) - h^{\prime}(x)g(x)}{h(x)^2}[/tex]

In this question:

Numerator [tex]g(x) = 5, g^{\prime}(x) = 0[/tex]

Denominator [tex]h(x) = 3 - x, h^{\prime}(x) = -1[/tex]

So

[tex]f^{\prime}(x) = \frac{0(3-x) - 5}{(3 - x)^2} = -\frac{5}{x^2-6x+9}[/tex]

The derivative is:

[tex]f^{\prime}(x) = -\frac{5}{x^2-6x+9}[/tex]

Answer:

x=31°

Step-by-step explanation:

2x-7+x+4 = 3x-3

90+3 = 3x

93 = 3x

x = 93/3

x = 31°

Answer:

-1

Step-by-step explanation:

mean, mu = 135.

Standard deviation = 20

X = 115

use the z score formula : [tex]z = \frac{x-mu}{standard deviation}[/tex]

to get (115-135)/20 = -1

Answer:

y-intercept is ( 0 , 5 )

Step-by-step explanation:

Answer:

C) 395.84 in^2

Step-by-step explanation:

I took the test

Step-by-step explanation:

10(2−4)+5=2−8

10(2x-4)+5=2x-810(2x−4)+5=2x−8

Solve

1

Distribute

10(2−4)+5=2−8

20−40+5=2−8

2

Add the numbers

3

Add 

35

3535

 to both sides of the equation

4

Simplify

5

Subtract 

2

2x2x

 from both sides of the equation

Answer:

97

Step-by-step explanation:

Answer:

Step-by-step explanation:

Explanations are below

Step 1

(100-3)  Observe the equation

Step 2

(100-3)  Simplify

100-(+3)

100-3

Answer: 97

Answer:

56°

Step-by-step explanation:

1st reason= alternate angles.

2nd reason= 124 and angle 6 is co-interior angles which means that little are shoudk adds up to 180.

180-124=56

Answer:

4,050 cubic feet

Step-by-step explanation:

The figure is made up of a square pyramid and cube

Therefore:

Volume of the figure = volume of the square pyramid + volume of the cube

✔️Volume of the square pyramid = ⅓*a²h

a = 15 ft

h = 9 ft

Volume of square pyramid = ⅓*15²*9 = 675 ft³

✔️Volume of the cube = s³

s = 15 ft

Volume of the cube = 15³ = 3,375 ft³

✔️Volume of the figure = 675 + 3,375 = 4,050 cubic feet

Answer:

AN*(B\C)=(ANB)\C=>ANB/C=ANB/C

Answer:

It's true but I don't know if my proof is technical enough for you.

Step-by-step explanation:

Multiplication and division of numbers can happen in any order.

Answer:

15 feet

Step-by-step explanation:

if the dog run is a rectangles then the formula for the perimeter is 2h+2l

if we plug in the numbers we know we get this:

2h+2(5)=40

2h+10=40

2h=30

h=15

Answer: Venus

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given diameters of planets:

Compared, we see the smallest value belongs to Mercury

The second smallest planet is Mars

Answer:

False

Step-by-step explanation:

Since its a bigger number in the negative, it means it further from zero which makes it false

Answer:

m<GLK = 58°

Step-by-step explanation:

Given:

m<GLH = 2x + 6

m<HLJ = x

Required:

m<GLK

Solution:

First, find the value of x

m<GLH + m<HLJ = 180° => Linear Pair Theorem

Substitute

2x + 6 + x = 180

Add like terms

3x + 6 = 180

3x + 6 - 6 = 180 - 6

3x = 174

3x/3 = 174/3

x = 58

m<HLJ = x = 58°

Thus, m<HLJ and m<GLK are Vertical angles.

Therefore:

m<GLK = m<HLJ (Vertical angles theorem)

m<GLK = 58° (Substitution)

Answer:

6 and 19

Step-by-step explanation:

x+2x+7=25

3x=18

x=6

the other number is 19

Answer:

Here ya go ! :)

Step-by-step explanation:

Given:

The table of values.

To find:

The least-squares regression line for the data set in the table by using the desmos graphing calculator.

Solution:

The general form of least-squares regression line is:

[tex]\hat{y}=mx+b[/tex]           ...(i)

Where, m is the slope and b is the y-intercept.

By using the desmos graphing calculator, we get

[tex]m\approx 2.55,b\approx -6.435[/tex]

Substitute these values in (i).

[tex]\hat{y}=(2.55)x+(-6.435)[/tex]

[tex]\hat{y}=2.55x-6.435[/tex]

Therefore, the correct option is A.

The graph of regression line is attached below.

The equation of regression line is [tex]y=2.55x-6.435[/tex]

A graphing calculator is a calculator device that has the ability to display plotted graphs for complex equations.

First we have to enter the given table in graphing calculator,

After entering the data given into table,

We get,   m= 2.55  and b= -6.435

So that, the equation of regression line is [tex]y=2.55x-6.435[/tex]

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Answer:

1440°

Step-by-step explanation:

the formula used for this is (n-2)×180° where n=# of sides in the polygon

Answer:13

Step-by-step explanation:plug in the the numbers

Answer:20

Step-by-step explanation:

I’m smart

Answer

number

4.D

5.B

6.C

Answer:

24 dollars

Step-by-step explanation:

each pound is $1.60 and 15 times $1.60 equals 24

Answer:

$24

Step-by-step explanation:

5/8=15/x

cross product

8*15=5*x

120=5x

x=120/5

x=24

[tex] \boxed{ \tt{the \: dimensions \: are : }}\\ \boxed{ \tt{b = 9 \: meters} }\\ \boxed{ \tt{l = 20 \: meters}}[/tex]

[tex]5 {s}^{2} = (3 + s) \times (14 + s) \\ 5 {s}^{2} = {s}^{2} + 17s + 42 \\ {4s}^{2} - 17s - 42 = 0 \\ s = \frac{ - ( - 17) + \sqrt{ {( - 17)}^{2} - 4(4)(42)} }{2(4)} \\ s = \frac{17 + 31}{8} \\ s = 6 \\ hence \to \:the \: dimensions \: are : \\ b = s + 3 = 6 + 3 = 9 \: meters \\ l = s + 14 = 6 + 14 = 20 \: meters[/tex]

The new dimensions of the pool are; Width = 9 and Length = 20.

A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.

It is given that the square pool was turned into a rectangular one and it's area was enlarged by a factor of 5 by enlarging one side of the pool by 3 meters and the other side by 14.

[tex]5s^2 = (3+s)(14 +s)\\\\5s^2 =s^2+ 17s + 42\\\\4s^2 - 17s - 42 = 0\\\\[/tex]

The root of the expression;

[tex]s = \dfrac{-(-17) + \sqrt{-17^2 - 4(4)(42)} }{2(4)} \\\\s = 6[/tex]

The dimensions are;

Width = 3 + s = 9

Length = 14 + s = 20

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Answer:

i) Mean = 1933.1817

ii) Range = 5684

iii) Third quartile = 6054

Step-by-step explanation:

Given data :

currency exchange rate : 1 AUD = 5.8 HKD

cost of each ounce = 2 AUD

Fixed shipping cost for each carton = 80 HKD

number of cartons = 20

next determine the total cost of the 20 cartons in HKD

= ∑(weight in ounce * cost of each ounce *exchange rate) +fixed shipping cost

= ∑ ( 160*2*5.8 + 80 )  + -------------- + (650 *2*5.8 + 80 ) ----------------- ( 1 )

= 81756 HKD

i) find the mean value ( X )

= Total cost / number of cartons

= 81756 / 20 = 4087.8

ii) Find the standard deviation

= [tex]\sqrt{\frac{(1936-4087.8)^2+-----+(7620-4087.8)^2}{20-1} }[/tex]      note: std =  √∑(xi-X )^2 / (n-1)

= 1933.1817

iii) Find the range

Range = highest cost - lowest cost   ( values gotten from equation 1 )

           = 7650 - 1936

           = 5684

iv) Determine the third quartile

third quartile = 6054

attached below is the detailed solution

Answer:

the easiest way to get these numbers is to graph the function, i use desmos.

Step-by-step explanation:

the axis of symmetry is -1

the vertex is -1, 0.5

the domain is all real numbers

the range is all real numbers that are <= 0.5

Answer:

4

Step-by-step explanation:

he will have extra but its better then having nothing , and only extra by 1

Answer: 4 packs

Step-by-step explanation: Dario need to buy 4 packs and get

4 ·6=24 cups

Answer:
48x + 96

Step-by-step explanation:

Given expression: 12(4x + 8)

Using the Distributive Property, we can simplify the given expression.

Distributive Property: [tex]a(b + c) = ab + ac[/tex]

Simplify:

[tex]\implies 12(4x+8)\\\\\implies 12(4x) + 12(8)\\\\\implies 48x + 96[/tex]

The expression that is equivalent to 12(4x + 8) is [tex]48x + 96[/tex].