Which of these fractions is largest A: 6 as a fraction of 30 B: 30 centimetres as a fraction of 2 metres C: 16 pence as a fraction of £1 ? You must show your working.​

The values for the composition of functions are:

a. (f o g)(x) = -x³ - x + 1

b. (g o f)(x) = -x³ - x - 1

Here, we have,

to Determine the Value of Composite Functions:

The value of composite functions are determined by first finding the output of the inner function, which would be used as the input of the outer functions to derive the value of the composite functions.

Given the following:

f(x) = x³ + x + 1

g(x) = -x

a. To find (f o g)(x), substitute g(x) as the inner function for x into f(x):

(f o g)(x) = (-x)³ + (-x) + 1

Simplify

(f o g)(x) = -x³ - x + 1

b. To find (g o f)(x), substitute f(x) as the inner function for x into g(x):

(g o f)(x) = -(x³ + x + 1)

Distribute by -1

(g o f)(x) = -x³ - x - 1

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complete question:

If f(x)=x³+x+1 and g(x)=-x, find (f°g)(x) and (g°f)(x).

(f°g)(x)=

Answer:

I helped you last time so I'll help you again.

Step-by-step explanation:

We can find the average rate of change of f(x) over the interval [10, 20] using the formula:

average rate of change = (f(b) - f(a))/(b - a)

where a = 10 and b = 20.

So, we have:

f(a) = f(10) = 1.85(10)^2 = 185

f(b) = f(20) = 1.85(20)^2 = 740

average rate of change = (740 - 185)/(20 - 10) ≈ 55.5

Therefore, the average rate of change of f(x) over the interval [10, 20] is approximately 55.5.

The matching table is given in the image below:

A scatter plot, an undeniably essential chart for visualizing the correlation between two variables, is constructed by putting one variable on the x-axis and another one alongside the y-axis, with each individual data point symbolizing both associated values.

Scatter plots are not only indispensable when inspecting trends and peculiarities in a given set of data but can likewise be applied to examine the relationship or link between the two components.

Essentially imperative to fields such as economics, engineering, and statistics, these diagrams are efficiently drawn up through popular software applications like Excel or Python.

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The difference in height of short and tall tower is 3 inch.

We have,

length of each block = 3/4 inch

So, the length of 5 block

= 5 x 3/4

= 15/4 inch

and, the length of 9 blocks

= 9 x 3/4

= 27/4 inch

So, the difference in height of short and tall tower is

= 27/4 - 15/4

= 12/4

= 3 inch

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Answer:

  (d)  (12, -34)

Step-by-step explanation:

You want the component form of the vector sum -3u +5v where u=(1,3) and v=(3,-5).

Add the corresponding parts of the scaled vectors. The scale factor applies to both vector components. (It works the same way as "dilation".)

  -3u +5v = -3(1, 3) +5(3, -5)

  = (-3, -9) +(15, -25) = (-3 +15, -9 -25)

  = (12, -34)

Volume of the prism given is 51 [tex]\frac{17}{40}[/tex].

The volume of the prism is given by the formula,

Volume of the prism = Base area × height

Base area = 2 3/4 × 5 1/2

                 = 11/4 × 11/2

                 = 121 / 8

Volume of the prism = 121 / 8 × 3 2/5

                                  = 121/8 × 17/5

                                  = 2057/40

                                  = 51 17/40

Hence the volume of the prism is 51 [tex]\frac{17}{40}[/tex].

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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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The solution is, the two dimensions  will be 2121.32 by 1414.2.

Here, we have,

let X and Y be the two dimensions.

Area will be X times Y.

XY = 3000000

Y = 3000000 / X

Perimeter = 2x + 3y

substituting the values:

Perimeter = 2x + 3*3000000 / x

               = 2x + 9000000 / x

so, we get,

2 = 9000000 / x^2

x^2 = 9000000 / 2 = 4500000

x = sqrt(4,500,000)

  = 2121.32

  = 1000 sqrt (4.5)

y = 3000000 / 2121.32

  = 1414.2

  = 1000 sqrt(2)

so the dimensions will be 2121.32 by 1414.2 .

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complete question:

A rancher wants to fence in an area of 3000000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?

There are 190 pages would be in a book with 19 chapters.

We have to given that;

The scatter plot shows the relationship between the number of chapters and the total number of pages for several books.

Now, We get;

For 19 chapters at x - axis,

The value of pages at y - axis is, 190

Thus, There are 190 pages would be in a book with 19 chapters.

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Answer:

it can be simplify as follows:

Answer:

890 as it is not divisible by 4

The annual premium is $192.5.

We have,

Number of units to be purchased by Alicia:

= 50,000 / 1,000

= 50 units

At age 30, the cost per $1,000 unit of insurance is $3.85 for a female.

= Number of units purchased x Premium per $1,000

= 50 x 3.85

= $192.5

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Answer:

  f(n) = 3^(n -1)

Step-by-step explanation:

You want a function that describes the relation shown in the table.

The values under Steps are sequential, which makes determining the function a lot easier.

The values listed under Black Triangles don't have a common difference, but they do have a common ratio:

  r = 3/1 = 9/3 = 27/9 = 3

For this function, we'll use 'n' as the independent variable (the number of steps), and we'll call the function 'f'.

For common ratio r and a pair of table values (n, f(n)) = (a, b), the exponential function can be written as ...

  f(n) = b·r^(n -a)

With r=3 and (a, b) = (1, 1), this becomes ...

  f(n) = 1·3^(n -1)

The multiplier 1 isn't really needed, so we can use ...

  f(n) = 3^(n -1)

We can use unit conversion to find the value of $1 in Euros:

\begin{aligned}

£1 &= $1.41 \\

\frac{£1}{1.15} &= \frac{$1.41}{x} \\

x &= \frac{$1.41}{\frac{£1}{1.15}} \\

&= $1.7278

\end{aligned}

Therefore, $1 is equal to €1.7278.

The cost for a new customer to rent a bay for 6 hours at Top Golf is $22, which includes a $10 player card fee and a $12 bay rental fee at $2 per hour.

Let's let "x" be the total cost for a new customer to rent a bay for 6 hours.

We know that there is a flat fee of $10 for the player card, and then an additional $2 per hour for the bay rental.

So, the equation for the cost "x" can be written as

x = 10 + 2(6)

The expression 2(6) represents the cost of the bay rental for 6 hours. We can simplify the expression by multiplying 2 and 6, which gives us

x = 10 + 12

Now, we can combine like terms to find the final cost

x = 22

Therefore, the cost for a new customer to rent a bay for 6 hours at Top Golf is $22.

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--The given question is incomplete, the complete question is given

" For a new customer top golf charges $10 for a player card and $2 per hour. Write and solve a linear equation to find the cost for a new customer to rent a bay for 6 hours."--

Salton City has a lower altitude because -60.96 meters is less than -38.1 meters.

Option C is the correct answer.

We have,

The altitude of Bombay Beach is -60.96 meters.

The altitude of Salton City is -38.1 meters.

Altitude is the height of a location above sea level, and a negative value indicates that the location is below sea level.

Therefore, we can see that Salton City has a higher altitude than Bombay Beach because -38.1 meters is a higher altitude than -60.96 meters.

Thus,

Salton City has a lower altitude because -60.96 meters is less than -38.1 meters.

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Answer: $34.01

Step-by-step explanation:

To get the answer, we must first add up the entire amount of money saved after four weeks of mowing the neighbor's lawn, then subtract the bike's price.

Since we get $40 a week, after 4 weeks we will have saved the following:

40 × 4 = 160

We will therefore have $160 to spend on the bike. The bike costs $125.99, so we will have the following amount of money after purchasing the bike:

160 - 125.99 = 34.01

Therefore, after purchasing the bike, we will have $34.01 leftover.

Answer:

approximately 183.4 square centimeters.

Step-by-step explanation:

We can use the formula for the circumference of a sphere, which is:

C = 2πr

where C is the circumference and r is the radius.

We know that the circumference of the pincushion is 24 cm. We can use this to find the radius:

C = 2πr

24 = 2πr

r = 24/(2π)

r ≈ 3.82 cm

Now that we know the radius, we can use the formula for the surface area of a sphere, which is:

A = 4πr^2

Substituting the value we found for the radius, we get:

A = 4π(3.82)^2

A ≈ 183.4 cm^2

Therefore, the surface area of the pincushion is approximately 183.4 square centimeters.

Answer: 67.65

Step-by-step explanation:

Multiply 3.0*4.1 and you get 12.3

Then take that sum and multiply it by the 5.5

So 12.3*5.5=67.65

The value of x, given that when it divides a number, there is a quotient and a remainder, is 400

To find the value of divisor, we can use a variant of the division algorithm formula :

Divisor = ( Dividend - Remainder ) / Quotient

x is the divisor

Dividend = 19, 432

Remainder = 232

Quotient = 48

This means that the value of x is:

x = ( 19, 432 - 232 ) / 48

x = 19, 200 / 48

x = 400

In conclusion, x is 400.

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Explanation for problem 14

There are 4 aces and 4 copies of "9".

4+4 = 8 cards we want to select out of 52 total

8/52 = (4*2)/(4*13) = 2/13  which points to choice D as the final answer

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

Explanation for problem 15

4 kings gives a probability of 4/52 = 1/13.

After the king is chosen, there are 52-1 = 51 cards left since we aren't replacing it. The probability of getting a queen on the second selection is 4/51

(1/13)*(4/51) = 4/663 is the probability of a king, then a queen, with no replacement. We arrive at choice C as the final answer.

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

Explanation for problem 16

face card = picture card

face card = Jack, Queen, King

aces are not considered a face card

3*4 = 12 face cards in total

A = 12/52 = (4*3)/(4*13) = 3/13 is the probability of selecting a face card.

That card is then put back (aka replacement) and we still have 52 cards in the deck. We don't drop down to 51.

13 hearts ---> B = 13/52 = 1/4 is the probability of getting a heart

A*B = (3/13)*(1/4) = 3/52 is the probability of getting a face card, then a heart, when replacement is done. The final answer is choice B

Answer:

The measure of angle E is 56°.

Answer: D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The equation of the ellipse with the foci is x²/36 + y²/(27) = 1.

The distance between the foci of an ellipse is calculated using the following formula;

c² = a² - b²

Where;

For this question, a = 6 and c = 3, the value of b is calculated as;

c² = a² - b²

3² = 6² - b²

9 = 36 - b²

b² = 27

b = √27

b = 3√3

The equation of the ellipse is calculated as;

x²/a² + y²/b² = 1

x²/36 + y²/(27) = 1

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The crocodile weighs 0.005 times as much as the hippopotamus.

To determine how many times as much as the hippopotamus a crocodile weighs, we need to compare the weights of both animals. However, they are currently in different units, so we need to convert them to a common unit.

We can convert the weight of the hippopotamus from tons to pounds by multiplying by 2,000, since there are 2,000 pounds in a ton. This gives us:

Hippopotamus weight = 2 tons × 2,000 pounds/ton = 4,000 pounds

Now that both weights are in pounds, we can compare them. To determine how many times as much as the hippopotamus the crocodile weighs, we can divide the weight of the crocodile by the weight of the hippopotamus. This gives us:

Crocodile weight / Hippopotamus weight = 20 pounds / 4,000 pounds = 0.005

Alternatively, we could say that the hippopotamus weighs 200 times as much as the crocodile.

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Answer:

The answer is 50% or 1/2

Step-by-step explanation:

There are four outcomes on that chart: 1,2,3,3

There are two threes which means 2/4=.5 or 1/2

Answer:

1/2 chance of landing on a 3.

Step-by-step explanation:

Out of the 4 sections on the spinner, 2 of them have the number 3. This means that there is a 2/4 chance that the spinner lands on a three. This fraction can be simplified into 1/2.

The simplified expression is:

8y + 4 - 3y + 12 = 5y + 16

Remember the distributive property:

A*(B + C) = A*B + A*C

Now let's look at our expression, it is:

8y + 4 - 3y + 12

We can reorder the terms to get:

8y - 3y +4 + 12

Now we can take y as a common factor:

(8 - 3)y + 4 + 12

Now simplify the two operations:

(8 - 3)y + 4 + 12 = 5y + 16

That is the expression simplified.

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Answer:

144π = (1/2)(4/3)π(r^3)

144 = (2/3)(r^3)

r^3 = 216, so r = 6 mm, meaning the diameter is 2 × 6 mm = 12 mm.