If you had six candy bars and you gave 12 people an equal piece, how much would
each person receive?

The terms given in US national debt in standard form when converted to scientific notation form will be 2.86 * 10^11, 3.70 * 10^11, 9.07 * 10^11, 3.23 * 10^12, 5.67 * 10^12 and 1.35 * 10^13 respectively.

Scientific notation if the process of conversion of very large numbers which are otherwise inconvenient to read into decimal form raised to some power of 10.

During this conversion, the numbers in standard form are written such that only one place value before decimal is left and written as coefficient and all other numbers are then counted and written in the form of base 10 raised to some exponent value.

The coefficient value must be such that its value lies between 1 and 9 and less than 10. Thus, the following numbers can be written as follows in scientific form.

286330760848.37 = 2.86 * 10^11

370918706949.93 = 3.70 * 10^11

907701000000.00 = 9.07 * 10^11

3233313451777.25 = 3.23 * 10^12

5674178209886.86 = 5.67 * 10^12

13561623030891.79 = 1.35 * 10^13  

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Answer:

the set of all real numbers -1≤y≤1

Step-by-step explanation:

according to the definition of 'sin'-function, the max value of it is '+1' and the min is '-1'. Finally, the correct answer is B. the set of all real numbers -1≤y≤+1.

Answer:

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = (x+1)³ - 2 = (x-(-1))³ - 2. Comparing this to f(x) = (x-2)³, we see that replacing x with x+3 in f(x) gives g(x) = (x+3-2)³ = (x+1)³, so this transformation moves the graph of f(x) three units to the left. Then, adding the constant -2 to f(x) translates the graph down 2 units. Finally, adding the constant 2 to the result of the previous step translates the graph up 2 units, so the graph of g(x) is obtained by first translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = √x - 2 + 1 = f(x-2) + 1. This means that the graph of g(x) is obtained by translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Step-by-step explanation:

Answer:

4*9

Step-by-step explanation:

It's obvious.

Answer:

The first and second choice since those symbols are the ones that apply to open circle on the number line and the 2 last ones are closed circles

Step-by-step explanation:

The symbols represented by the open circle on the number line are greater than ( > ) and less than ( <). The correct options are A and B.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

On the number line, the open circle stands for the symbols greater than (>) and less than (<). These symbols are used to form inequalities also.

Therefore, the symbols represented by the open circle on the number line are greater than ( > ) and less than ( <). The correct options are A and B.

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Scale factor back to original size = 1/7

        7x and 7 years.

This means the original size will be;

Length = 7x × 1/7

Width = 7y × 1/7

Hence, the scale factor will be 1/7 back to the original size.

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Answer:

(a) Yes, E and F are independent events.

(b) P(E and F) = P(E)P(F) = (1/2)(1/2) = 1/4

The expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

The amounts of packets of crisps purchased are given as follows:

The expression for the total number of packets of crisps that Jane buys is given by the addition of these two amounts.

Hence the expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

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Answer:

Step-by-step explanation:

$100x0.5x1=$5

Answer:

92 km

Step-by-step explanation:

by calculator hope it gelps

9 km — 1 cm

225 km — 225 : 9 = 25 cm

Answer:

\(x^4-12x^3+54x^2-108x+81\)

Step-by-step explanation:

We have been given the following binomial expansion for (a + b)⁴:

\(\boxed{(a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4}\)

To use this to expand and simplify (x - 3)⁴, first identity the values of a and b:

Substitute the values of a and b into the expansion, and simplify:

\(\begin{aligned}(x-3)^4&=x^4+4x^3(-3)+6x^2(-3)^2+4x(-3)^3+(-3)^4\\\\&=x^4+4x^3(-3)+6x^2(9)+4x(-27)+81\\\\&=x^4-12x^3+54x^2-108x+81\end{aligned}\)

The solution to the system of equations is 3x + y = -19 and -3x + 3y = 3 is (-5, -4)

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

3x + y = -19

-3x + 3y = 3

Next, we plot the graph of the system (see attachment)

Using the graphing function on a calculator, we have the solution to be

(-5, -4)

This is so because the equations 3x + y = -19 and -3x + 3y = 3 intersect at the point (-5, -4) and they are not equivalent equations

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Answer:

448 miles

Step-by-step explanation:

Amy's car can hold 15 gallons of gas. Provided that each gallon can drive her 32 miles. This means that 15 gallons can drive her 480 miles.

15 gallons x 32 miles = 480 miles

However, she needs to keep 1 gallon of gas in the tank for safety reasons. So we have to subtract 1 gallon from 15 gallons.

15 gallons - 1 gallon = 14 gallons

Now, let's compute again.

14 gallons x 32 miles = 448 miles

Amy can drive 448 miles before she needs to fill up the tank again.

The expression of logarithmic function, f(x) = ln (1/gᵏ) after all possible expansion is equals to the f(x) = - k × ln( g).

In mathematics, the logarithmic function is defined as inverse function to exponent function and defined as f(x) = logₐx where a is base of function. Properties of Logarithmic Functions :

We have, a natural logarithmic function, i.e., base = 10, f(x) = ln (1/gᵏ) and we have to expand it. To expand logarithms means write them as a sum or difference product of logarithms. The order to apply rules is quotient rule, product rule and then power rule. So, f(x) = ln (1/gᵏ)

applying quotient rule,

=> f(x) = ln(1) - ln( gᵏ)

Appling power rule,

=> f(x) = ln(1) - k ln( g)

Applying Zero Exponent Rule,

=> f(x) = 0 - k × ln( g)

Hence, the required expansion is f(x) = - k × ln( g).

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Answer:

the answer is A

Step-by-step explanation:

add 17 to both sides

Answer:

120(2x² + 3x - 2) or 240x² + 360x - 240

Perimeter = 64x + 28

x = 3

Length = 60ft

Width = 50ft

Step-by-step explanation:

Area = (12x + 24)(20x - 10)

= 12(x + 2).10(2x - 1)

= 120(2x² + 3x - 2)

= 240x² + 360x - 240

Perimeter = 2(12x + 24) + 2(20x - 10)

= 24x + 48 + 40x - 20

= 64x + 28

64x + 28 = 220

64x = 192

x = 3

Length = 12(3) + 24

= 36 + 24

= 60

Width = 20(3) - 10

= 60 - 10

= 50

Answer:

Step-by-step explanation:

The area of the building is given by the formula ...

  A = LW

  A = (12x +24)(20x -10) . . . . . substitute given length and width

__

The perimeter is twice the sum of length and width:

  P = 2(L +W)

  P = 2((12x +24) +(20x -10)) = 2(32x +14)

  P = 64x +28

__

If the perimeter is 220 feet, we can use that fact to find the value of x.

  220 = 64x +28

  192 = 64x . . . . . . . subtract 28

  3 = x . . . . . . . . . . . divide by 64

Then the dimensions of the building are ...

  length = 12x +24 = 12(3) +24 = 60 . . . feet

  width = 20x -10 = 20(3) -10 = 50 . . . feet

The length and width of the building are 60 feet and 50 feet, respectively.

Answer:

69

Step-by-step explanation:

Since the values in the data set has been ranked already from smallest to largest, as shown in the question.

Then calculate the index,

To find the 36th percentile using the data set,

Multiply k (36/100) by n (25) to reach an index of 9.

Then since the index is whole number,

To calculate percentile according to the 'greater than' method, count the values in the data set from smallest to largest until you reach the number ranked 9th

Which is 69.

Since the value for the 36th percentile must be greater than the first nine values, the 10th ranked value would be the kth (36th) percentile. In this data set, that value is 69.

Alternatively, using the 'greater than or equal to' method, after getting the 9th rank,

Include the ninth-ranked value, (69) in this data set.

The kth (36th) percentile is then calculated by taking the average of that value in the data set (69) and the next ranked value (69). (59 + 69) / 2 = 69.

Answer: A

Step-by-step explanation:

\(\left(\frac{f}{g} \right)(x)=\frac{f(x)}{g(x)}=\frac{\sqrt[3]{4x}}{2x+3}\)

The denominator cannot equal 0, so \(x \neq -\frac{3}{2}\).

Answer:

The height of the model should be 36 cm

Step-by-step explanation:

The ratio given by the scale "2 cm : 1.5 m", is what we need to use to write a proportion and solve for the unknown height "h". This means that 2 cm is to 1.5 meters, as "h" cm is to 27 meters, which can be written in math form with the following proportion, and solved for the unknown:

\(\frac{2\,cm}{1.5\,m} =\frac{h}{27\,m} \\\frac{2\,*\,27}{1.5} \,cm\\h= 36\,cm\)

Answer:

  60

Step-by-step explanation:

In the function, the growth factor is "a", the base of the exponent. When the exponent is increased by 1, the value is multiplied by "a".

  f(7) = a·f(6) = 4·15

  f(7) = 60

_____

As you know, the exponent signifies repeated multiplication. So, an increase of 1 in the exponent means the base is part of the product one more time:

  a^6 = a·a·a·a·a·a

  a^7 = a·a·a·a·a·a·a = a·(a^6)

Answer:

120,000 ft^3

Step-by-step explanation:

step 1: 20ft times 150ft is 3000ft.

step 2: 3000ft times 40ft^3 is 120,000ft^3

Using the constant of proportionality the value of x when y is 72 is 9.

What is a COP?

The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.

If y varies directly as x, it means that y can be expressed as a constant multiple of x, i.e., y = kx, where k is the constant of proportionality.

To find k, we can use the given information that y = 48 when x = 6 -

y = kx

48 = k(6)

k = 8

Now that we know k, we can use it to find x when y = 72 -

y = kx

72 = 8x

x = 9

Therefore, when x = 72, the value of x = 9.

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1. The Pythagoras theorem is (6+r)² = r²+9²

2. 36+12r+r² = r²+9²

3. The value of r is 3.75

Pythagoras theorem states that; the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

This means that, c² = a² + b²

In the triangle, 6+r is the hypotenuse, 9 and r are the other two legs.

therefore;

(6+r)² = r²+9²

= (6+r)(6+r) =r²+9²

36+6r+6r+r² = r²+9

36+12r+r² = r²+9

Collecting like terms

12r+r²-r²= 81-36

12r = 45

r = 45/12

r = 3.75

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Answer:

1.5

Step-by-step explanation:

The possible perimeters are 140 feet, 148 feet and 160 feet.

In order to determine the width that would be used to determine the possible perimeters, the formula for the area would have to be rewritten.

A rectangle is a 2-dimensional quadrilateral with four right angles and two diagonals that bisect each other at right angles.

Area of a rectangle = length x width

Width = area / length

1200 / 40 = 30 feet

1200 / 50 = 24 feet

1200 / 60 = 20 feet

Perimeter of a rectangle = 2 x (length + width)

Perimeter when width is 30 feet : 2(40 + 30) = 140 feet

Perimeter when width is 24 feet : 2(24 + 50) = 148 feet

Perimeter when width is 20 feet : 2 (20 + 60) = 160 feet

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