The area of the arctic ocean is about 5 millon square miles. this is about 16% of the area of which ocean pacific 64 million square miles or indian 25 million square miles

SOLUTION:

For inequalities, the solution to is usually where the two regions meet.

The graphs here are:

Final answer:

The final answer here is Option (B)

The factors of the given monomial are given below

What is a monomial?

A monomial is, broadly speaking, a polynomial with just one term in mathematics. There are two definitions of a monomial: A monomial, often known as a power product, is a product of powers of variables with nonnegative integer exponents, or a product of variables with repeats. The constant 1 is a monomial, which means that it is equivalent to the empty product and to for any variable x. If just one variable, x, is examined, a monomial is either 1 or a power xn of x, where n is a positive integer. If many variables, say x,y,z, are examined, each can be assigned an exponent, such that each monomial has the form xaybzc with a,b,c non-negative integers.

The factors of the monomial 16x²y are 2.2.2.2.x.x.y

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The factors of the monomial are given below

What is a monomial?

A monomial is, broadly speaking, a polynomial with just one term in mathematics. there are two definitions of a monomial: A monomial, often known as a power product, is a product of powers of variables with nonnegative integer exponents, or a product of variables with repeats. The constant 1 is a monomial, which means that it is equivalent to the empty product and to for any variables x. If just one variable, x, is examined, a monomial is either 1 or a power xn of x, where n is a positive integer, if many variables, say x, y, z, are examined, each can be assigned an exponent, such that each monomial has the form xaybzc with a, b, c non-negative integers.

The factors of the monomial 16x²y are 2.2.2.2.x.x.y

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Both Sheila and Bob together can wash the car in 10 minutes

Calculating work :

The formulas to find work and time is given by

Time Taken = 1 / Rate of Work

Rate of Work = 1 / Time Taken

If a work can be done in x number of days, then the work can be done in one day = 1/x

Total Work done = Number of Days × Efficiency ( of the person or machine )

Given that,    

Sheila can wash her car in 15 minutes

Let us consider washing the car is 1 unit of work

Then the work can done by Sheila in 1 minute = 1/15  

Bob take twice as long as Sheila to wash the same

Bob can wash the same car in 30 minutes

Then the work can done by Bob  in 1 minute = 1/30  

From above calculation,

The work can be done by Sheila and Bob = (1/15 + 1/30)

= (2+1) /30 = 3/30 = 1/10  

So the efficiency of Both Sheila and Bob per minute = 1/10

Let Both can complete the work in x minutes

As we know Total Work done = time × Efficiency

⇒ 1 = x × 1/10

⇒ x = 1 × 10

⇒ x = 10 minutes

Therefore,

Both Sheila and Bob together can wash the car in 10 minutes

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Answer:

10.8

Step-by-step explanation:

Hello!

Once, graphed, a right triangle forms, with PQ as the hypotenuse. The other two lengths are 6 and 9.

We can use the Pythagorean theorem: [tex]a^2 + b^2 = c^2[/tex]

The length of PQ is 10.8.

2.6

Given the expression;

Simplify the expression in the bracket to have:

Simplify the result to have;

Hence the result of the given function on simplification is 2.6

Three pairs of siblings from different families can be seated in two rows of three chairs so that siblings may not sit next to each other in the same row, and no child may sit directly in front of their sibling in 96 ways.

There are 3 pairs of siblings. We can name them as a₁, a₂, b₁, b₂, c₁ and c₂, a total of 6 children.

There are 2 rows of 3 seats each.

We will try to find the number of ways each seat can be filled.

So considering the first seat in first row, it can be filled in 6 different ways. Because any one from 6 children, say a₁, can be seated.

Now for the second seat in first row can only be filled by one of b₁, b₂, c₁ or c₂ because the first seated child a₁ along with the sibling a₂ of the same cannot be seated in the second seat. So in 4 different ways.

For the third seat remaining in the first row, one out of the remaining  pair of siblings c₁ or c₂ can be seated. This can be done in 2 ways.

Now after filling the first row in this manner, the second row can be filled in only 2 ways.

So total number of ways the children can be seated = 6 x 4 x 2 x 2 = 96 ways

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Answer:

The actual area of the warehouse would be:

[tex]72000~\text{feet}^{2}[/tex]

Step-by-step explanation:

Step 1:  Convert all the blueprint lengths into real lengths:

Each inch in the blueprint represents 20 feet in the real world.

So, the real-life length (18 inches in blueprint) would be:

[tex]1~\text{inch}= 20~\text{feet}\\\\\text{Multiply by 18 on both sides}:\\1\times18~\text{inch}= 20\times18~\text{feet}\\18~\text{inch}= 360~\text{feet}\\[/tex]

Similarly, the real-life width would be:

[tex]1~\text{inch}= 20~\text{feet}\\\\\text{Multiply by 18 on both sides}:\\1\times10~\text{inch}= 20\times10~\text{feet}\\10~\text{inch}= 200~\text{feet}\\[/tex]

Step 2: Calculate the area

The area of the warehouse would be given by:

[tex]\text{Area}=\text{Length}\times \text{Width}[/tex]

The length is 360 feet, and the width is 200 feet, so the total area would be:

[tex]\text{Area}=\text{Length}\times \text{Width}\\\\\text{Substitute the values for the length and width}\\\text{Area}= 360\times 200\\\text{Area}=72000[/tex]

Answer:

A = {KL}

Step-by-step explanation:

The subset of the sample space that represents the complement of the event in which Joe plays in the first match is A = {JL, KL}

It is a branch of mathematics that deals with the occurrence of a random event.

The sample space of this experiment consists of all possible ways of choosing two names from a group of three.

Since the order in which the names are chosen does not matter, the size of the sample space is given by the number of combinations of 3 things taken 2 at a time, which is 3.

The three possible outcomes are: {JK, JL, KL}.

If we want to find the complement of the event in which Joe plays in the first match, we need to find the outcomes in which Joe does not play in the first match.

There are two such outcomes: JL and KL.

Therefore, the subset of the sample space that represents the complement of the event in which Joe plays in the first match is A = {JL, KL}

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Answer:

2 1/2 (D)

Step-by-step explanation:

1 8/12 + 5/6

you have to make the denominator on the right equal to the denominator on the left. in order to do that, multiple the numerator and denominator on the left my two.

5/6 become 10/12.

1 8/12 + 10/12

1 18/12

Simplify,

2 6/12 (1/2)

Answer:

[tex]1\frac{8}{12}+\frac{5}{6}=2\frac{1}{2}[/tex]

Answer: 2x^2

Step-by-step explanation:

    (x+5)

 x (2x - 9)

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

X times 2x = 2x^2

Height of the triangle is = 14m

Given,

Base of the triangle is 8m

Area of the triangle is = 56m^2

To find the height of the triangle.

Now, According to the question:

We know that

Area of the triangle is = 1/2 x b x h

where, b = base

h = height

Plug all the values of base and area in above formula:

56m^2 = 1/2 x 8m x h

56 x 2 / 8 = h

h = 14m

Hence, Height of the triangle is = 14m

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The identified scale factor of the triangles is 71 / 37.

Scale factor is the ratio of corresponding sides on two similar figures.

The triangles are similar. Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Therefore, let's identify the scale factor of the triangles.

The triangle on the right is a scale copy of the triangle on the left.

Hence,

scale factor = 71 / 37 = 71 / 37

Therefore, the scaled factor of the triangles in fraction form is 71 / 37

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Hello,

Two parallel lines have the same slope, which means that our line's slope, will also be 1.2.

So now we have a point and a slope, so we can use the following formula to find the equation of the line:

y-y1 = m (x-x1)

Where:

y1 - y coordinate of a point on the line

x1 - x coordinate of the same point on the line

m - slope

Plugging in we get:

y+3 = 1.2 (x-0)

y = 1.2x - 3 (slope intercept form)

or

5y-6x = -15 (standard form)

Cheers

Answer:100 cm

Step-by-step explanation: first, you would find the area of the whole rectangle.

L x W = A

10x14=140

Next, find the area of the unshaded part. To do this, you would subtract 6 from 14

14-6=8

After that, times 8 by 10, then divide by 2

10x8=80

80÷2=40

Take 40 and subtract it from the area of the whole rectangle

140-40=100

The perimeter of the given equilateral triangle would be 28.2 cm if the sides of the triangle are 9.4 cm.

The numerical value that is rounded up to represent the supplied value's next value serves as its upper bound.

The numerical number that is rounded off for the previous value or the predicted value of the provided value is the lower bound for the supplied value.

The sides of an equilateral triangle are 9.4 cm

The perimeter of an equilateral triangle = 3 × length of the side

The perimeter of an equilateral triangle = 3 × 9.4

The perimeter of an equilateral triangle = 28.2 cm

Hence, the perimeter of the given equilateral triangle would be 28.2 cm if the sides of the triangle are 9.4 cm.

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Answer:

y=8X

Explanation:

The ratio 13 to X = 13:X

The ratio 104 to y = 104:y

If they are equivalent, we have that:

We write the ratios in fraction form.

We then make y the subject of the equation.

We can simplify further to get:

This is the equation that represents y in terms of X.

The given polynomials are as ,

We have to subtracrt these given polynomials,

Option D is correct.

The volume of a cone is given as follows;

The volume of the cone with the given dimensions is

1,046,666.67 cubic feet (rounded to the nearest hundredth)

Without approximation, the answer would be,

1,046,666.6666 cubic feet

Given the graph of the parabola

AS shown in the figure

The coordinate of the vertex is the point (2.5, 2.25)

so, the answer will be:

the vertex of the function shown below is located at (2.5, 2.25)

The probability that joe and jane end up in the same class is 0.3258 .

In the question ,

it is given that

90 students is to be split into 3 equal size classes , so ,

the three classes  will have 30 students each .

let these classes be Class A , Class B and Class C .

Let Joe and Jane be in Class A .

the total number of ways of selecting 30 students for class A from 90 students is C(90,30) .

Since , we have fixed Joe and Jane in Class A , the remaining 28 spots of class A can be filled by remaining 88 students  in C(88,28) ways ,

So , the probability that Joe and Jane end up in the same class is

= C(88,28)/C(90,30) .

Since there are three  classes ,

the required probability is 3*C(88,28)/C(90,30) .

= 3×[tex]\frac{88!}{28!*60!}[/tex]×[tex]\frac{60!*30!}{90!}[/tex]

= 29/89

= 0.3258

Therefore , the probability that joe and jane end up in the same class is 0.3258   .

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The initial velocity = vi = 6m/s

The final velocity = vf = 16 m/s

The total time = t = 20 seconds

The rate of change in velocity is called acceleration (a) that can be written as:

or

Put the values in the equation to get the value of 'a'.

or

hence, the value of a is 1/2.

Answer

Part A

(g o h)(x) = x - 1

Part B

Domain of (g o h) = (-∞, ∞)

Explanation

Part A

We are given that

g(x) = x² + 3

h(x) = √(x - 4)

We are then asked to find (g o h)(x)

To do that, we need to note that (g o h)(x) means we write g(x), but instead of x, we write h(x). That is,

(g o h)(x)

= g(h(x))

= [h(x)]² + 3

= [√(x - 4)]² + 3

= x - 4 + 3

= x - 1

Part B

To find the domain

The domain of a function refers to the values of the independent variable (x), where the dependent variable [y or f(x)] or the function has a corresponding real value. The domain is simply the values of x for which the output also exists.

And for (g o h)(x) = x - 1, we know there will be an answer for all real number values of x. Hence,

Domain = (-∞, ∞)

Hope this Helps!!!

Answer:

Hour elapsed 0 1 2 3 4

Grams 1986 1032.7 537 279.2 145.2

Explanation:

To find the amount left after 1 hour, 3 hours, and 4 hours, we need to find the common ratio.

Since we know the initial amount and the amount left after 2 hours, the ratio of these quantities is the square of the common ratio, so

r² = 537/1986

r² = 0.2704

r = √0.2704

r = 0.52

Then, the amount left after 1 hour is the initial amount multiplied by the common ratio, so

For 1 hour

Amount left = 1986(0.52) = 1032.7 grams

In the same way, the amount left after 3 and 4 hours is

For 3 hours

Amount left = 537(0.52) = 279.2 grams

For 4 hours

Amount left = 279.2(0.52) = 145.2 grams

Therefore, the complete table is

Hour elapsed 0 1 2 3 4

Grams 1986 1032.7 537 279.2 145.2

Answer:

Step-by-step explanation:

-1>-4>-6

-1 is the greatest number.

Answer:

a₉₀ = 168

Step-by-step explanation:

there is a common difference between consecutive terms, that is

- 8 - (- 10) = - 6 - (- 8) = 4 - (- 6) = 2

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 10 and d = 2 , then

a₉₀ = - 10 + (89 × 2) = - 10 + 178 = 168

The table of values for the given equation is presented below:

x       y

-3    17

-2   2

-1    -7

0   -10

1    -7

2    2

3    17

The Standard form for a quadratic equation is  ax²+ bx + c=0, where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

To solve a quadratic function, you should find the discriminant: D=b²-4ac and then use this variable in the formula: [tex]x=\frac{-b \±\sqrt{\Delta} }{2a}[/tex].

The given equation is a quadratic function because have a degree equal to 2. Then, when you plot the graph, you obtain a parabola.

First, you should replace the given values for x in the equation y=3x²-10

x        y

-3   y=3*(-3)²-10= 3*9-10=27-10=17

-2   y=3*(-2)²-10= 3*4-10=12-10=2

-1    y=3*(-1)²-10= 3*1-10=3-10= -7

0    y=3*(0)²-10= 3*0-10=-10= -10

1     y=3*(1)²-10= 3*1-10=3-10= -7

2    y=3*(2)²-10= 3*4-10=12-10= 2

3    y=3*(3)²-10= 3*3-10=27-10= 17

Now, you have the points to draw the graph, show the attached image.

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Given the function f(x), we can write it like this:

Using the formula for polynomial derivatives, we get:

Therefore, the derivative f'(x) is 12/x^5