katrina can arrange the chairs in the classroom in 5 minutes. one day peter helped her and took both of them 2 minutes to arrange the chairs. how long will it take peter to arrange the chairs all by himself?

Answer:

80%

Step-by-step explanation:

you're occupying 800 out of 1000

the way to write this mathematically is to write: 800/1000,

which equals 0.8

then to make this a percentage you x100

and your answer is 80%

Using the law of indices, [tex]1024^{\frac{2}{5} } = 16[/tex]

The expression can be solved using the law of indices as follows:

[tex]1024^{\frac{2}{5} }[/tex]

using law of indices, involving bracket.

Brackets with indices are where we have a term inside a bracket with an index (or power) outside of the bracket.

To do this we can raise everything inside the bracket to the power.

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

Therefore,

1024 = 2¹⁰

Hence,

[tex]2^{\frac{2}{5} (10)} = 2^{\frac{20}{5} } = 2^{4} = 16[/tex]

Therefore,

[tex]1024^{\frac{2}{5} } = 16[/tex]

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The given function y = x³ is not a linear function but a cubic function.

For the given function;

y = x.x.x

This, can be written, after adding the power of x as;

y = x³

Now, put x = 1; y = 1

Put x = 2; y = 8

Put x = 3; y = 27

This will not form a straight line but a cubical curve.

As, the function is not changing linearly but cubical.

Thus, the function is not linear function.

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The simplified form of the given expression ( a⁴b²c³d ) / acbd is equal to (a³bc² ) .

As given in the question,

Given expression :

 ( a⁴b²c³d ) / acbd

Simplified form of the given expression using rules of power and exponents:

Since this is division of algebraic fractions, the index (power or exponent) of the like literals in the numerator and denominator are to be subtracted. Thus index of variable a reduces from 4 to 1. Similarly index of variable b reduces from 2 to 1 and that of c reduces from 3 to 2. Lastly variable d remains in the denominator as there is no corresponding factor in the numerator.

( a⁴b²c³d ) / acbd

= (a⁴⁻¹ )(b²⁻¹ )(c³⁻¹ )(d¹⁻¹)

= a³ bc²d⁰

= a³bc²

Therefore, the simplified form of the given expression ( a⁴b²c³d ) / acbd is equal to (a³bc² ) .

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Answer:

16

Step-by-step explanation:

gof(-6) means g(f(-6))

f(-6)=-(-6)-2

=6-2=4

g(4)=4^2=16

When two amounts are proportionate, they fluctuate at the same rate, maintaining the constancy of their relationship.

Here x be the proportionality constant  its value 5.5.

Matthew bought 2 movie tickets for $11,

Rosa bought 7 movie tickets for $38.50.

let the value of per ticket is x

2x = 11 and 7x = 38.5

7x- 2x = 38.5 -11

x = 5.5

here x be the proportionality constant  its value 5.5.

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The answer is x = 1, assuming that the space is meant to be an equal sign.

Answer:x=1

Step-by-step explanation:

you would have to distribute the 5 into the (x+4)

then it would be

5x+20-3^2=2^4

then do the exponents

5x+20-9+16

then add 9 by both sides

5x+20=25

then subtract 20 on both sides

5x=5

then divide 5 on both sides

x=1

then check your work by putting 1 for x and you get 2^4=16

Answer:

Step-by-step explanation:

find x :

5( x + 4 ) - 3^2 = 2^4

5x + 20 - 9 = 16

5x = 16 - 20 + 9

5x = 5

x = 5 : 5

x = 1

----------------

check

5(1 + 4) - 3^2 = 2 ^4

25 - 9 = 16

16 = 16

the answer is good

Answer:

200k

Step-by-step explanation:

4x50=200

The cost of buying 4 kg of potatoes at 50k per kg is 200k.

To calculate the cost of buying 4 kg of potatoes at 50k per kg, you can simply multiply the weight (4 kg) by the price per kilogram (50k).

Cost = 4 kg * 50k per kg

Now, perform the calculation:

Cost = 200k

So, the cost of buying 4 kg of potatoes at 50k per kg is 200k.

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Answer:

23-i

Step-by-step explanation:

Multiply using the FOIL method and after that combine the real and imaginary parts of the expression.

Answer:

8000 times 2x times 1

Step-by-step explanation:

(8 times 10^3) (2xtimes 10^1)

8 times 10^3=8000

= 8000 times 2x times 1

= 160000x

Answer:

y = 5

Step-by-step explanation:

2(40 - 5y) : 80 - 10y

10y + 5(1 + y) : 5y + 5

80 - 10y = 5y +5

-10y = 5y -75

-10y - 5y = 5y - 75 - 5y

-15y/-15 = -75/-15

-15y/-15 : y

-75/-15 : 5

Hence, The answer should be 5

 (-7,∞) &  (−∞, 1/2] are the interval notation.

What is interval notation in math?

8x-5>=6x-1 or 4+4x<=3x-3

8x-5 ≥6x-1

8x - 5 ≥ 6x - 1

8x - 6x ≥  5 - 1

 2x ≥  1

   x ≥  1/2

Therefore, x could be any number less than or equal to 1/2. In interval notation, this looks like

 (−∞, 1/2]

4+4x ≤ 3x-3

4 + 4x ≤  3x - 3

4x - 3x ≤  -3 - 4

   x ≤  -7

Therefore, x could be any number less than -7 , but x couldn't be -7, since that would make the two sides of the inequality equal. In interval notation, this looks like:

   (-7,∞)

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Answer:

The measure of the largest angle is 145°

Step-by-step explanation:

Since the angles form a linear pair taking two angles that add to 180 and solving for x will give you the answer. the sentence "One angle is 5 more than four times the size of the other angle." your equation should look like this:

5 + 4x. the other angle uses the variable x. So the equation 5 + 4x + x = 180 should result in x = 35. That saying, the smaller angle is 35 and to find the larger angle either plug in x or subtract 180-35. both shoukd result in 145° which is the larger angle.

The number of elements that are there in the sample space is 6.

It should be noted that sample space simply means the collection or the set of possible outcomes that are in the random experiment.

From the information, in the special deck of cards has 10 cards. four are green, three are blue, and three are red.

Therefore, the sample space will be:

S = GH, GT, BH, BT, RH, RT

It should be noted that H and T represents the head and tail.

Therefore, there are 6 elements.

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The expression that will give a value of 74 is C. (75 - 5) × 1 + 4.

It should be noted that an expression is used to how the relationship between the variables that are expressed in the data or information given.

In this case, we want to find the expression that will give a value of 74. This will be :

= (75 - 5) × 1 + 4

= 70 × 1 + 4

= 70 + 4

= 74

The correct option is C.

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Answer: yes then no

Step-by-step explanation:

Answer:

4 inches

Step-by-step explanation:

the cube has a volume (V) calculated as

V = s³ ( s is the side length )

given V  = 64 , then

s³ = 64 ( take the cube root of both sides )

s = [tex]\sqrt[3]{64}[/tex] = 4

side length is then 4 inches

The sales in 2012 is estimated to be $40546.5 million if we use the midpoint formula assuming that the sales followed a linear pattern.

Midpoint is a term used in geometry and can be described as the center or middle point of a line segment. It enables you to take two endpoints, and then by using these endpoints you can find the point that is midway between them in the line segment.

Considering,

[tex]P_{1} = (x_{1},y_{1})[/tex]

[tex]P_{2} = (x_{2},y_{2})[/tex]

Here;

[tex]x_{1}[/tex] = 2010

[tex]x_{2}[/tex] = 2014

[tex]y_{1}[/tex] = $35,109 million

[tex]y_{2}[/tex] = $45,984 million

The formula for the midpoint is given as;

[tex]P_{m}[/tex] = {( [tex]x_{1} + x_{2}/2[/tex] ), ( [tex]y_{1} + y_{2} / 2[/tex] )}

[tex]P_{m}[/tex] = {(2010 + 2014 / 2), (35109 million + 45984 million / 2)}

[tex]P_{m}[/tex] = {(4024 / 2), (81,093 million / 2)}

[tex]P_{m}[/tex] = {2012 , 40546.5 million}

Therefore, the sales in 2012 are calculated to be $40546.5 million by using the midpoint formula.

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Answer:

-0.54, 5.54

Step-by-step explanation:

[tex]x^2-5x-3=0 \\ \\ x=\frac{5 \pm \sqrt{25+12}}{2} \\ \\ x=\frac{5}{2} \pm \frac{\sqrt{37}}{2} \\ \\ x \approx -0.54, 5.54[/tex]

Answer: m<1 = 151     m<2 = 29         m<3 = 151

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:\angle1 = 151° [/tex]

[tex]\qquad \tt \rightarrow \: \angle2 = 29 \degree[/tex]

[tex]\qquad \tt \rightarrow \: \angle3 = 151 \degree[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

We can use angle pairs of intersecting lines to find the remaining angles :

[tex]\qquad \tt \rightarrow \: \angle4 + \angle1 = 180 \degree[/tex]

[ linear pair ]

[tex]\qquad \tt \rightarrow \: 29 \degree + \angle1 = 180 \degree[/tex]

[tex]\qquad \tt \rightarrow \: \angle1 = (180 - 29) \degree[/tex]

[tex]\qquad \tt \rightarrow \: \angle1 = 151\degree[/tex]

next,

[tex]\qquad \tt \rightarrow \: \angle2 = \angle4[/tex]

[ by vertical opposite angles ]

[tex]\qquad \tt \rightarrow \: \angle2 = 29 \degree[/tex]

and,

[tex]\qquad \tt \rightarrow \: \angle3 = \angle1[/tex]

[ by vertical opposite angles ]

[tex]\qquad \tt \rightarrow \: \angle3 = 151 \degree[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Employee's gross pay is their salary before any payroll deductions such as taxes, benefits, and other expenses are made.

Her goss weekly pay is $409.13.

Before taxes, benefits, and other payroll deductions are deducted, an employee's gross pay is what they are paid.

Net pay, often known as take-home pay, is the sum that is left over after all deductions have been taken into consideration.

Federal income tax:

306.36+ 43 = 349.36

Medical insurance:

349.36 + 22.35 = 371.71

Credit union:

371.71 + 25 = 396.71

State tax:

396.71 increased by 1.5% is 396.71 * (1.015) = 402.66

Local tax:

402.66 increased by 1.5% is 402.66 * (1.015)= 409.13

Her goss weekly pay is $409.13.

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a a a a a a a a a a a a a a a aa a a

In mathematics, an operation is a function that transforms 0-n operands or parameters into a known output value. The number of operands affects how complicated the operation is. 90.95 feet per second equates to 62 miles per hour.

An operation in mathematics is the function that converts 0–n parameters or operands into definite output value. The complexity of operation depends on how many operands there are.

The operations that are the most frequently studied are binary operations (i.e., operations of the arity 2), which include addition and multiplication, and the unary operations (i.e., operations of the arity 1), which include additive inverse and the multiplicative inverse. A zero-arity operation, also known as nullary operation, is a constant. An illustration of ternary operation, also known as an operation of arity 3, is the mixed product.

Usually, it is considered that arity is constrained. Even so, the infinitary operations are occasionally considered, in which case "normal" finite dimensionality operations are referred to as finiteary operations.

A partial operation is described as being similar to operation but using a partial function in place of a function.

1miles/hour= 1.467feet/second

62 miles/ hours= 62*1.467feet/second

                        = 90.95 feet/second

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A rock climber throws a first aid kit to the another climber who is higher up the mountain, the initial velocity of the kit is 12 m/s at an angle of 71 above the horizontal, at the instant when the kit is caught, it is traveling horizontally, so its vertical speed is zero, height difference between climbers is 0.85 m.

Velocity is the direction at which an object is moving and serves as a measure of the rate at which its position is changing as seen from a specific point of view and as measured by specific unit of time (for example, 60 km/h northbound). In kinematics, area of classical mechanics that deals with the motion of bodies, velocity is a fundamental idea.

Vertical motion of the first aid kit:

The Initial vertical velocity, u = 5.70 sin 45.7 = 4.08 m/s

Acceleration, g = -9.81 m/s²

When climber who is higher up the mountain catches the kit it's vertical speed is zero.

Final vertical velocity, v = 0 m/s

We have the equation of motion, v² = u² + 2as

Substituting

0² = 4.08² + 2 x -9.81 x s      

s = 0.85 m

So kit travels 0.85 m vertically.

Height difference between the climbers = 0.85 m.

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The monetary value of gold, silver and bronze is $0.5, $0.35 and $0.25 respectively.

The given conditions in the question are-

Let the monetary value of gold be 'a'.

Let the monetary value of silver be 'b'.

Let the monetary value of bronze be 'c'.

The total monetary value is $20.

The equation will be;

14 gold, 20 silver, and 24 bronze

14a + 20b + 24c = 20      .......eq1

20 gold, 15 silver, and 19 bronze

20a + 15b + 19c = 20   .......eq 2

30 gold, 5 silver, and 13 bronze.

30a + 5b + 13c = 20       .....eq 3.

Solving equation 1,2 and 3 by elimination method.

a = 1/2

b = 7/20 and

c = 1/4

Thus, the monetary value of gold, silver and bronze is $0.5, $0.35 and $0.25 respectively.

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FINDING THE DIFFERENCE WE SUBRACT

[tex]8 - 4 \\ = 4[/tex]

FINDING THE QUOTIENT WE DIVIDE

[tex]8 \div 4 \\ = 2[/tex]

HOPE THIS HELPS