Which inequality correctly orders the numbers -2/5, -11/3 and -2.5?

The expression similar to  [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex] obtained by using the laws of indices is option A.

A. [tex]2\cdot x^2 \cdot y\sqrt[3]{7\cdot x \cdot y^2}[/tex]

According to some of the laws of indices, we have;

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

[tex]x^m \cdot x^n = x^{m+n}[/tex]

[tex]\sqrt[m]{x^n} =x^{\frac{n}{m} }[/tex]

The expression can be presented as follows; [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex]

Simplifying the above expression gives;

[tex]\sqrt[3]{56\cdot x^7\cdot y^5 } = \sqrt[3]{8 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 }[/tex]

[tex]\sqrt[3]{8 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 } = \sqrt[3]{2^3 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 }[/tex]

Collecting terms with an index of a multiple of 3 gives;

[tex]\sqrt[3]{2^3 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 } = \sqrt[3]{2^3\cdot x^6 \cdot y^3 \times 7\cdot x \times y^2 }[/tex]

[tex]\sqrt[3]{2^3\cdot x^6 \cdot y^3 \times 7\cdot x \times y^2 } = 2\cdot x^2 \cdot y \times \sqrt[3]{ 7\cdot x \cdot y^2 }[/tex]

The expression that is equivalent to  [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex]is option A.

A. [tex]2\cdot x^2 \cdot y \times \sqrt[3]{ 7\cdot x \cdot y^2 }[/tex]

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Answer:

x<6

Step-by-step explanation:

2x/3<4

2x<12

x<6

Answer:

x < 6

Step-by-step explanation:

[tex]\frac{2x}{3}[/tex] < 4 ( multiply both sides by 3 to clear the fraction )

2x < 12 ( divide both sides by 2 )

x < 6

A floor that is 3 3/4 yards wide and 5 1/2 yards long requires 20 5/8 square yards of hardwood flooring area.

length = 5 1/2 yd, breadth = 3 3/4 yd.

Make fractions out of both measurements first.

3 3/4 = 3 + 3/4

= 12/4 + 3/4

= 15/4

5 1/2 = 5 + ½

= 10/2 + ½

= 11/2

Area = (15 * 11)/(4 * 2) yd2

Area = 165/8 yd2

They essentially believed that 165/8 = 20 leftover 5 area = 20 5/8 yd2.

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Answer:

Step-by-step explanation      a=0.32

The required simplified value of x in the given expression is 8.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
2.8x + 10 + 5.7x = 70+x

Simplifying,
8.5x + 10 = 70 + x
8.5x - x = 70 - 10
7.5x  = 60
x = 60 / 7.5
x = 8

Thus, the required simplified value of x in the given expression is 8.

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Betsie should buy the 250 envelopes from the shop Letter2go.

As, 250 envelopes will cost £31.9 in Shop Letter2go whereas will cost £33.17 in Shop Value World.

Given, that Betsie is going to buy 250 envelopes.

the cost of envelopes in two shops:

Value World:

Pack of 10 envelopes for £1.99

Buy 2 packs get 1 pack free

Letters2go:

Pack of 25 envelopes for £3.19

Now, if we see the cost of envelopes in shop 1 i.e. Value World

Cost of Pack of 10 envelopes = £1.99

Also, 1 pack is free for 2 packs

1 pack = £1.99

2 packs = 2×£1.99 = £3.98

Also, with 2 packs Betsie get 1 pack free

so, Betsie gets 3 packs for £3.98.

1 pack = 10 envelopes

3 packs = 30 envelopes.

Hence, In shop Value World:

30 envelopes = £3.98

1 envelope = £3.98/30

250 envelopes = (3.98/30)×250

So, 250 envelopes will cost £33.17 in Shop Value World.

And in shop Letter2go:

25 envelopes = £3.19

1 envelope = £3.19/25

250 envelopes = (3.19/25)×250

So, 250 envelopes will cost £31.9 in Shop Letter2go.

Hence, 250 envelopes will cost £33.17 in Shop Value World and £31.9 in Shop Letter2go.

So, Betsie should buy the 250 envelopes from the shop Letter2go.

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The correct answer to this question is d. the value of the 6 in 364 is 10 times the value of the 6 in 346.

The place value of the 6 in 346 is six because it is in the place of ones, whereas the place value of the sixth in 364 is 60 because it is in the place of tens. As a result, the value of 60 is ten times that of the value of 6.

The value of each digit in a number is known as place value. Every digit in a number has a distinct value depending on where it is located. The value of a digit depends on its position in the number, which can result in a number having two similar digits with different values.

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Answer:

[tex]\frac{4+\sqrt{11} }{5}[/tex]

Step-by-step explanation:

to rationalise the denominator, multiply the numerator and denominator by the conjugate of the denominator.

the conjugate of 4 - [tex]\sqrt{11}[/tex] is 4 + [tex]\sqrt{11}[/tex] , then

[tex]\frac{1(4+\sqrt{11}) }{(4-\sqrt{11})(4+\sqrt{11}) }[/tex] ← expand denominator using FOIL

= [tex]\frac{4+\sqrt{11} }{16-11}[/tex]

= [tex]\frac{4+\sqrt{11} }{5}[/tex]

The equation  y = 4x - 8 is discrete

Discrete data is a sort of numerical information that consists of full, concrete numbers with predetermined, set values that can be counted.

While complex numbers and fluctuating data values taken over a predetermined period of time are examples of continuous data.

The main distinction between continuous and discrete data is that the former has a finite value that can be counted while the latter has an endless number of possible values that can be measured.

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The probability that the proportion of politicians who are lawyers will be less than 40% is 0.009299 .

Given :

Population Proportion ( p ) = ( 44 % ) = 0.44

Sample proportion ( p hat ) = ( 40 % ) =  0.4

Size of sample ( n ) = 853

To find : P ( p hat < 0.4 )

Formula : ( p hat - p ) / [tex]\sqrt{ p * ( 1 - p ) / n }[/tex]

Substituting values in the above formula ,

z = ( 0.4 - 0.44 ) / [tex]\sqrt{ 0.44 * ( 1 - 0.44 ) / 853}[/tex]

z = - 2.3535

z - score = -2.3535

Finding the p - value :

p - value = 0.009299

Therefore , the probability that the proportion of politicians who are lawyers will be less than 40% is 0.009299 .

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Answer:

25.5 feet because of some

Step-by-step explanation:

.,........

Answer:

Step-by-step explanation:

The table (D) values would produce the same graph as shown.

Mathematical structures known as graphs are used to describe pairwise relationships between things. Graph theory is the study of these mathematical structures. Vertices (also known as nodes or points) and edges are what make up a graph in this sense (also called links or lines). It is possible to distinguish between directed and undirected graphs, where edges connect two vertices asymmetrically and symmetrically, respectively. One of the primary topics in discrete mathematics is graphs.

From the graph, find the intercepts,

At x = 0, the value of y is -1.

At, y = 0, the value of x is 4

So, from the given options, we can see that the values are given in table (D).

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a) The average life of the lot is 1078.33 hrs, b) the total life is 107833.33 hours, c) a proportion of 1/2 bulbs have a life exceeding 1000 hrs while d) an estimation of 50 bulbs have a life exceeding 1000 hours.

It is given that the number of bulbs in a given lot is 100.

The number of bulbs in the sample selected is 6

The life of the sample bulbs was

no.         life (hours)

1                      950

2                     1210

3                     1070

4                      840

5                     1420

6                      980

a)

The average life of the bulbs can be calculated by

the sum of the lives of the sample/ no. of samples

= (950 + 1210 + 1070 + 840 + 1420 + 980) / 6

= 1078.3333 hrs

b) The total lives of the bulbs in the lot will be

average life X no. of bulbs

= 1078.3333 X 100

= 107833.33 hrs

c)

We can gain the proportion of the bulbs that have a life exceeding 1000 hrs by the given sample

The bulbs

2, 3, and 5 have lives exceeding 1000 hrs.

Hence, out of 6 bulbs, 3 have lives exceeding 1000 hrs.

Therefore the proportion

= 3/6

= 1/2

d)

The number of bulbs in the lot with a life exceeding 1000 will be

proportion X no. of bulbs

= 1/2 X 100

= 50 bulbs

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The rent for seven months is 35000 and a tenant hire the room for Rs 55,000 at the same rate of rent for 11 months

The rent of a room for 4 months is Rs 20,000.

The rent of a room for 1 month is Rs 20,000./4

The rent of a room for 1 month is Rs 5000

The rent of a room for 7 months is Rs 5000 x 7

The rent of a room for 7 months is Rs 35000

Now we need to calculate the number of month a tenant hire the room for Rs 55,000 at the same rate of rent

The rent is 5000 for 1 month

The rent will be 55000 for 1/5000 x 55000 = 11 months

Therefore, the rent for seven months is 35000 and a tenant hire the room for Rs 55,000 at the same rate of rent for 11 months

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The amount that each person should pay is  $22.06   .

in the question ,

it is given that

total number of persons = 3 person + 1 = 4 persons

cost of the meal = $72.50

sales tax percent = 6.75%

tip percent = 15%

So , the amount of sales tax = 6.75% of cost = 0.0675 * 72.50 = $4.89

and , the amount of tip is = 15% of cost

= 0.15 * 72.50

= 10.87

So , the total amount payable is = cost + sales tax + tip

= 72.50 + 4.89 + 10.87

= 88.26

since the total number of persons is 4 ,

the amount per person is = 88.26/4 = 22.06

Therefore , The amount that each person should pay is  $22.06   .

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Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.

The ratio of an object's mass to its volume is its density. Grams per cubic centimeter, or g/cm³, are frequently used to measure density. Keep in mind that a volume is measured in cubic centimeters, not gram (the same volume as 1 milliliter). More particles will make a box denser than fewer particles in the same box. Despite the fact that the SI unit of density is kg/m³, we instead use g/cm³ for solids, g/ml for liquids, and g/L for gases out of convenience. The relationship between a substance's mass and the volume it occupies is known as its density.

Given,

Volume = 2.5 cm³

Mass = 10 g

For density:

Mass ÷ volume

10 ÷ 2.5

4

Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.

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Answer:

5 hours

Step-by-step explanation:

$65 - $15 = $50

$50/$10 = 5

Answer: you are left with 17.1 or 17.10

HOW TO:  picture this. i'ma going to go to your store and you have 27 dollars. you owe me 9.90 for some reason. you give me the money and i go on my way. how much money are you left with?

Answer: Either C. or D.But I'm sure it's D.

Step-by-step explanation:

The selling price of the the purse in a department store is cents.

For the given question-

A purse in such a department store costs $12.50 at wholesale.

The purse will be 140% more expensive at the store.

Then,

140% of 12.50 = 140 x 12.50 / 100

140% of 12.50 = 17.5

Selling price  = percent increase + cost price

Selling price  = 17.5 + 12.5

Selling price  = $30.0

Selling price  = 3000 cents

Thus, the selling price of the the purse in a department store is cents.

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The state population as a single-digit time power of 10 is approximately 4 × 10⁷.

Calculations are made easier and more realistic when a number is estimated, which is a plausible estimation of its true value.

To estimate something is to approximate it as accurately as possible.

To acquire a quick and approximate response is obtained by rounding down the values used in the computation.

Given the state estimated population = 38,332,521

Divide and multiply by 10

So,

= 3,833,252.1 × 10¹

= 383,325.21 × 10²

So, similarly, we can write

= 3.8332521 × 10⁷

So, we can write the state population as approximately 4 × 10⁷

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As corresponding angles ∠5 and ∠8 are equal. Hence line x is parallel to line z by converse of corresponding angles theorem.

What does converse of corresponding angles theorem states?

If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.

How can we show two lines are parallel to each other?

We can show lines are parallel by finding a pair of corresponding angles that are congruent.

Proving if two lines are parallel then third line is parallel too.

According to the given data:

       Therefore, ∠5 ≅ ∠7 (i.e. corresponding angles)

       ∠5 = ∠7

       ∠6 ≅ ∠8 (Corresponding angles are equal)

        ∴ Measure of angles is also equal ⇒ ∠6 = ∠8

       ∠5 = ∠8 (transitive property of equality of angles which says if

                               ∠a = ∠b and ∠b = ∠c then ∠a = ∠c)

       ∠5 ≅ ∠8 (If measure of angles is same then they are congruent)

Therefore, line x || line z

(Converse of the Corresponding Angles Theorem).

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The equation of the line through (3,1) and is perpendicular to a line through (6, -2) and (-8 ,5) is y = 2x - 5  .

In the question ,

it is given that

the required line is perpendicular to the line passing through (6, -2) and (-8 ,5) .

the slope is = (5 -(-2))/(-8 -6)

= 7/(-14)

= -1/2

so , the slope of the required line is = 2 .

The equation of the line passing through the point (3,1) with slope 2 is

(y - 1) = 2*(x-3)

y -1 = 2x - 6

y = 2x - 6 + 1

y = 2x - 5

the equation of line is y [tex]=[/tex] 2x - 5

the perpendicular slope is = 2

the y intercept is -5 .

Therefore , The equation of the line through (3,1) and is perpendicular to a line through (6, -2) and (-8 ,5)  is y = 2x - 5 .

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Step-by-step explanation:

The answer is: A=210÷26.2=8.2

B=now we have to turn minutes in to haurs 210:60=3.5 now 26.2÷3.5=29.7

Answer:

A) 26.2/210= .125 miles per minute

B) 210/26.2= 8.02 minutes per mile

C) the other runner talks about the same rate as b), not a).

Step-by-step explanation:

A)[tex]\frac{26.2}{210\\}[/tex] and B)[tex]\frac{210}{26.2}[/tex] :)  

C)the runner was referring to the time they took to run one mile, so the other runner ran 10 minutes to cover one mile, or as they say, "10 minute miles", which is the rate in minutes per mile.

If they were referring to the rates in a), that would imply the other runner ran 10 miles per minute... which is very unlikely.

Answer:

if the root is 10 then the function is ²✓5

The solution for x in the function when the equation  y=−4x+12 equals -12 is -6

From the question, we have the following equation that can be used in our computation:

y=−4x+12

To make the equation legible, we need to rewrite it

So, we have the following representation

y = −4x + 12

Also from the question, we have

y = -12

This means that we calculate x when y = -12

Substitute the known values in the above equation, so, we have the following representation

-12 = -4x + 12

So, we have the following equation

-4x + 12 = -12

Add -12 to both sides of the equation

So, we have the following representation

-4x + 12 - 12 = -12 - 12

Evaluate the like terms in the equation

-4x = -24

Divide both sides of the equation by -4

x = 6

Hence, the solution is 6

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Possible question

The equation below describes a function of x . y=−4x+12

Solve for x when y = -12

Answer:

$2825,32

Step-by-step explanation:

Value of the car after 1 year

$3000 * 3% = 3000 * 0.03 = 90

3000 - 90 = $2910

Value of the car after 2 year

$2910 * 3% = 2910 * 0.03 = 87.3

2910 - 87.3 = $2912,7

Value of the car after 3 year

$2912,7 * 3% = 2912,7 * 0.03 = 87.381

2912,7 - 87.381 = $2825,319

"Round to the nearest cent"

$2825,32

The length of the shorter leg is 9 mm.

The length of the longer leg is 12 mm.

The length of the hypotenuse is 15 mm.

Pythagoras theory applies to every right triangle. If

Step-by-step explanation:

Known

Asked

Answer

[tex]a^2 + b^2 = c^2[/tex]

[tex]a^2 + (a+3)^2 = (a+6)^2[/tex]

[tex]a^2 + a^2 + (2 \times a \times 3) + 3^2 = a^2 + (2 \times a \times 6) + 6^2[/tex]

[tex]2a^2 + 6a + 9 = a^2 + 12a + 36[/tex]

[tex]2a^2 - a^2 + 6a - 12a + 9 - 36 = 0[/tex]

[tex]a^2 - 6a - 27 = 0[/tex]

[tex]a^2 - 9a + 3a - 27 = 0[/tex]

[tex]a \times (a - 9) + 3 \times (a - 9) = 0[/tex]

(a-9) (a+3)=0

a-9=0  or  a+3= 0

a=9     or  a=-3 (impossible)

Shorter leg

a=9 mm

Longer leg

b = a+3

b = 9+3

b = 12 mm

Hypotenuse

c = a+6

c = 9+6

c = 15 mm

Probability that the product of the numbers on the top faces is prime is  1/2(1/6)⁴.

In everyday speech, the term "probability" refers to the likelihood that a specific event (or group of events) will take place, represented as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty). Statistics is the study of events that follow a probability distribution. Probability is a way to gauge how likely something is to happen. Even while no event can be foreseen with absolute certainty, probability can be used to convey how likely it is that it will happen.

Given,

12 fair dice rolled,

Probability that the product of the numbers on the top faces is prime:

⁶C₅ × (1/6)⁵ × ³C₁/⁶C₁

6 × (1/6)⁵ × 3/6

1/2(1/6)⁴

Probability that the product of the numbers on the top faces is prime is  1/2(1/6)⁴.

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Step-by-step explanation:

so, we have

6x² + 8xy + 8y²

and

5x² + 3xy + 16y²

we can combine only terms of the same kind (defined by the type and exponent of the used variables).

this is like adding fruit.

e.g. when we have a mixture of 3 apples, 4 oranges and 5 plums, and we add a mixture of 6 apples, 2 oranges and 3 plums - what do we get ?

we get a new mixture of

3+6 = 9 apples

4+2 = 6 oranges

5+3 = 8 plums

and exactly the same thing happens with mixing terms when adding them up.

so, we get

6+5 = 11x²

8+3 = 11xy

8+16 = 24y²

so, the result is

11x² + 11xy + 24y²

it is really that simple.