9. Given: f(x) = 2x + 3 and g(x) = 3x + 1
Find: (f • g)(-1)

Based on the number of movies that each of the 8 students saw in the past year, the mean number of movies is 12.875 movies

To find the mean of a distribution of numbers such as the number of movies seen in the past year, sum up the number of movies watched and then divide it by the number of students.

The mean number of movies watched by the students is therefore:

= Sum of movies watched / Number of students

= (6 + 14 + 14 + 16 + 14 + 18 + 15 + 6) / 8 students

= 103 / 8

= 12.875 movies

Rest of the question is:

Find the mean number of movies that the students saw.

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It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.

In the given statement is:

λ = 2.5 x 10^-2 [tex]min^{-1}[/tex]is the rate constant of the nucleus

To solve this problem, we use

N(t) = [tex]N_{0}[/tex]e^-λt

and since we are looking for the time it takes to decay the nucleus to one -fourth of its original amount, we set

N(t) = 1/4 [tex]N_{0}[/tex] = 0.25[tex]N_{0}[/tex]

We can substitute this in the decay equation:

0.25[tex]N_{0}[/tex] =[tex]N_{0}[/tex] e^-λt

Cancel the like terms

0.25 = e ^-λt

Take the natural logarithm of both sides:

㏑(0.25) =㏑(e^-λt)

㏑(0.25)= -λt

Solve for the time t:

t = - ㏑(0.25)/λ

Substitute the given rate constant :

t = ㏑(0.25) / 2.5 x 10^-2 [tex]min^{-1}[/tex]

t = -1.3863 /2.5 x 10^-2 [tex]min^{-2}[/tex]

t = 55.452mins

It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.

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Answer:

22 - 4x

Step-by-step explanation:

4(3-x) + 10  Distribute the 4

4(3) - 4x +10

12 - 4x +10

22 - 4x

The length of the new garage will be approximately 8.83 meters.

The length is referred as the side of a rectangle or a square. Ideally we use length to measure the larger side of a rectangle, but for a square all sides are equal and so can be called length.

The are of a square is given by the square of any side .

Given the area of the square is 52 square meters.

The new are of the square is 50% more.

Increased amount =  50% of 52 = 26 meters²

New area of square = 52 + 26 meters² = 78 meters²

Now we know that the area of a square is given by (side)² .

Therefore  (side)²= 78

or, side = √78

or, side = 8.8317...

or, side ≈ 8.83 meters

Therefore the length of the new garage is approximately 8.83 meters.

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Answer:

AC = 15

AB = 3

BC = 12

Step-by-step explanation:

AB + BC = AC

3x + (4x + 8) = 5x + 10

3x + 4x - 5x = 10 - 8

2x = 2

x = 1

AC = 5x + 10 = 5(1) + 10 = 15

AB = 3x = 3

Bc = 4x + 8 = 12

The value of constant v is 3.75 if y varies directly as x and when

x = 8 and y = 30.

Let v be any constant.

According to the given question.

y varries directly as x.

⇒ y ∝ x

⇒ y = vx                    (beacuse v is constant)

Here, it is give that x = 8 and y = 30.

Thereofre, the value of constant v when y = 30 and x = 8 is given by

y = vx

⇒ 30 = v(8)

⇒ 30/8 = v

⇒ v = 3.75

Hence, the value of constant v is 3.75 if y varies directly as x and when

x = 8 and y = 30.

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The simplified form of the expression is equivalent to 3c - 19

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as the addition, subtraction, division and multiplication.

Given the expression below;

2 (1.5c - 2.5) + 7 + 17

Expand

2(1.5c) - 2(2.5) + 7+ 17

3.0c - 5.0 + 24

3c - 19

Hence the simplified form of the expression is equivalent to 3c - 19

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Answer:

U = 4

Step-by-step explanation:

We take 3/9 and simplify it, making 1/3.

We multiply both by 12 to eliminate denominators, so the new numbers are 4 and U.

U = 4

The number that is halfway between the numbers -46.3 and 46.31 will be 46.305.

We are given the two numbers:

- 46.30 and 46.31

Now, we need to find a number that is halfway between the given numbers.

For this, we need to find the mid point between the two numbers that is given to us.

Mid point is calculated as:

| x | + | y | / 2

Substituting the values in the expression, we get that:

46.3 + 46.31 / 2

= 92.61 / 2

= 46.305

Therefore, we get that, the number that is halfway between the numbers -46.3 and 46.31 will be 46.305.

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Volume is equal to [tex]a^{3}[/tex] where an is the width or length of its edges.

The number of cubic units that a cube totally occupies is determined by its volume. The cubic unit of measurement for the volume of a cube includes [tex]centimetres^{3}[/tex], [tex]metres^{3}[/tex], [tex]inches^{3}[/tex], [tex]feet^{3}[/tex], etc.

A solid three-dimensional figure with 6 square faces or sides is known as a cube. The total amount of space a cube takes up is its volume. The cube's square shape means that all of its sides are square, and as a result, all of its edges would be of equal length. As a result, the cube's length, breadth, or height are all equal.

If a cube's length, breadth, and height are equal to "a," then;

Cube volume = a[tex]\times[/tex]a[tex]\times[/tex]a.

Therefore, Volume of cube is [tex]a^{3}[/tex] where a is the length of the edge.

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The function rule for g(x) is g(x) = -4x

The function is given as

f(x) = 4x

The transformation is given as reflection across the x-axis

The rule of this transformation is

(x, y) = (x, -y)

So, we have

g(x) = -f(x)

This gives

g(x) = -4x

Hence, the function rule for g(x) is g(x) = -4x

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Greetings from Brasil...

For rotation, we can use the expression:

Let rotate 180° - specifically for this angle, 180°, either counterclockwise or clockwise

SEN 180 = 0 and COS 180 = - 1

V(X; Y) → V'(- X; - Y)

V(0; - 2) → V'(0; - (- 2))

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Answer:

(-2, 32, -21)

Step-by-step explanation:

You just multiply B by 3 and then subtract the corresponding parts. For example -2 -(0*3). and then 14-(-6*3)

Answer:

slope=y2-y1/x2-x1

=-6-(-6)/9-6

=0/3

any fraction in which numerator is 0 is 0.

The hypothesis is called the alternative hypothesis test.

According to the statement

We have to explain about the alternative hypothesis.

So, For this purpose, we know that the

The alternative hypothesis is one among ll|one amongst |one in every of} two mutually exclusive hypotheses in a hypothesis test. the choice hypothesis states that a population parameter doesn't equal a specified value.

From the given information:

she randomly selects houses during this neighborhood and compares their estimated market price within the current year to their estimated value within the previous year. suppose that data were collected for a random sample of 8 houses, where each difference is calculated by subtracting the market price of the previous year from the value of the present year.

Then

the alternative hypothesis test usually suggests that there's an opportunity of variation (difference) within the data observed.

Hence, since we are told the "real real estate agent believes that the values of homes within the neighborhood she works in have increased (the chance of variation) from last year," which "each difference is calculated by subtracting the market price of the previous year from the market price of this year," we are able to reach the conclusion that this can be an example of an alternate hypothesis test.

So, The hypothesis is called the alternative hypothesis test.

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Answer:

A) The percentage of the bacteria increasing each hour is 15% per hour

B) When t=0 the population of bacteria is 3000 bacteria

C) After 24 hours the a sensible degree of accuracy in population is about 85875 (since only whole numbers count)

Step-by-step explanation:

A) To find the percentage of the bacteria increasing each hour the growth rate needs to be determined. To find it you need to subtract 1.15 by since the formula for exponential growth is a(1+r)^t one is added to the rate so to inverse it 1.15 needs to be subtractied by one to get 0.15. At this point you found the decimal rate to find the percentage you multiply 0.15 by 100 to make it a whole number and it results in 15%

B) To determine the size if the population when t=0 you substitute the variables t for 0 to get 3000×1.15^0 to get 3000 (remember anything times 0 is 0). Another way is to keep in mind that 3000 is the initial amount because that's the number with no variable with it.

C) To find the population after 24 hours substitute t for 24. After substituting t and multiplying 3000×1.15^24 the exact answer is 85875.52857. To find the answer in a sensible degree of accuracy you would round it to the nearest whole number which is 85876 since the dight in the tenths place is 5 or greater than the answer is rounded up by one.

Answer:

$2.08 per pound  

Step-by-step explanation:

1.52+1.08= 2.6pound

6.50/2.6=$2.5 per 2.6 Ibs

(turn the pound to a whole number)

2.6/2= 1.3 so 2,6/1.3= 2Ibs

(what you do to one side must be done to the other)

$2.5/1.3 =2.08

Answer:

false

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

to determine if (9, 10 ) is a solution, substitute x = 9 into the equation and if y = 10 then it is a solution.

y = 2(9) - 8 = 18 - 8 = 10

then (9, 10 ) is a solution of the equation

well, let's convert the mixed fraction to improper fraction firstly, then let's check their difference.

[tex]\stackrel{mixed}{15\frac{3}{5}}\implies \cfrac{15\cdot 5+3}{5}\implies \stackrel{improper}{\cfrac{78}{5}}\qquad \impliedby \textit{that's for just 1 day} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\LARGE after 6 days}}{\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} }\implies \cfrac{468}{5} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{change in bushels}}{\cfrac{468}{5}~~ - ~~\cfrac{78}{5}}\implies 78\qquad \impliedby \textit{so 6 days later he's got 78 more bushels}[/tex]

Answer:

Step-by-step explanation:

the number is y

you are told

y+0.5y=27

Therefore,

1.5y = 27.

If you divide by 1.5 on both sides, you'll get 18 which is your answer.

18+9=27

The relative frequency of adults who are engaging in less than the minimum amount of recommended moderate-intensity physical activity weekly is 92.16%.

The term 'relative' refers to an event that is being thought of in relation to or in proportion to another event.

As, per the given question.

The minimum standard for moderate-intensity aerobic activity weekly is 150 min.

All the values which are less than 150 min will be considered as the below specified standard for moderate-intensity aerobic activity.

The relative frequency for 0 - 49 min is 47.54%.

The relative frequency for 50 - 99 min is 32.77%.

The relative frequency for 99 - 149 min is 11.85%.

Thus, the cumulative of all relative frequencies will be;

= 47.54% + 32.77% + 11.85%

= 92.17%

Therefore, the percentage of adults who get less than the recommended amount of moderate-intensity physical activity per week is 92.16%.

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The complete question is -

The center for disease control and prevention (cdc) states that adults should engage in at least 75 min of vigorous-intensity aerobic activity or 150 min of moderate-intensity aerobic activity weekly. researchers gathered data from a random sample of adults who participated in the 2011–2012 national health and nutrition examination survey (nhanes).

What is the relative frequency of adults who are engaging in less than the minimum amount of recommended moderate-intensity physical activity weekly (less than 150 min)? Give your answer to two decimal places.

Answer: ( -2, 4)

Step-by-step explanation:

Answer:

AC = 8

BC = 10

AH = 4.8

Step-by-step explanation:

A = 1/2(AB)(AC)

24 = 1/2(6)(AC)

AC = (24)(2)/(6) = 8

BC^2 = AB^2 + AC^2 = 6^2 + 8^2 = 36 + 64 = 100

BC = 10

A = 1/2(AH)(BC)

24 = 1/2(AH)(10)

AH = (24)(2)/(10) = 48/10 = 4.8

Answer:

Step-by-step explanation:

Convert 576 from base 10 to following bases:

first of all  convert 576 from base 10 to base 2 we got this

1001000000_2

now  then convert  576 from base 10 to base 3 we got this

210100_3

now then convert 576 from base 10 to base 4 we got this

21000_4

now then convert 576 from base 10 to base 5 we got this

4301_5

now then convert 576 from base 10 to base 6 we got this

2400_6

now then convert  576 from base 10 to base 7 we got this

1452_7

now then convert 576 from base 10 to base 8 we got this

1100_8

now then convert 576 from base 10 to base 9

710_9

Only in base 5 does it end in 1.

referred by  www.web2.0calc.com

So only in base 5 does it end in final digit of 1.

A Binary operation can be considered as a function whose input is two elements of the same set S and whose output also is an element of S. S . Two elements a and b of S can be written as a pair (a, b) of elements in S.

So first of all convert 576 from base 10 to following bases:

first of all  convert 576 from base 10 to base 2 we will get this 1001000000_2

Then convert  576 from base 10 to base 3 we will get this 210100_3

Then convert 576 from base 10 to base 4 we will get this 21000_4

Then convert 576 from base 10 to base 5 we will get this 4301_5

Then convert 576 from base 10 to base 6 we will get this 2400_6

Then convert  576 from base 10 to base 7 we will get this 1452_7

Then convert 576 from base 10 to base 8 we will get this 1100_8

Then convert 576 from base 10 to base 9 we will get this 710_9

Therefore only in base 5 does it end in final digit of 1.

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4.8 packages will need for the use of one year.

No. of used packages of printer paper during 10 months = 4 Packages

As we know that there is 12 months in a year,

To determine the number of packages need for the year, first we have to find the number of package is being use in one month.

S0,  No. of used package in 1 month = 4/10 = 0.4 Package

Now, we will determine the number of packages for the use of one year, by multiplying the No. of used package in 1 month with 12.

No. of packages for the use of one year = 12 × 0.4

                                                                   = 4.8 Packages

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Polynomials which have (x-4) as a factor are a. x³ - 13x - 12 = 0 and c. x³ + 6x + 5x - 12 = 0.

An algebraic equation having two or more than two terms is called a polynomial.

According to the given question we have determine which of the following polynomials have (x-4) as a factor.

One way is factoring each of these polynomials.

Another way is given x - 4 is a factor,

∴ x - 4 = 0

x = 4 must satisfy the polynomial which has a factor of (x-4).

Now we have to replace x with 4 in each of the given polynomials and if LHS = RHS then (x -4) is a factor.

a. x³ - 13x - 12 = 0

(4)³ - 13(4) - 12 = 0

64 - 52 - 12 = 0

64 - 64 = 0. (LHS = RHS).

b. x³ + 8x² + 19x + 12 = 0

(4)³ + 8(4)² + 19(4) + 12 ≠0

Here you don't need to calculate further because in LHS sum of these terms won't be zero.

c. x³ + 6x + 5x - 12 = 0.

x³ + 11x - 12 = 0.

64 + 44 - 12 ≠ 0.

d. x³ - x² - 10x - 8 = 0.

64 - 16 - 40 - 8 = 0.

64 - 64 = 0, (LHS = RHS).

e. x² - 4

16 - 4 ≠ 0.

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The linear function that represents the line giving by the point slope equation y-2=4(x-3) is f(x) = 4x - 10

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

Also note that f(x) = y

Isolate the y then add 2 from both sides:

y - 2 = 4(x-3)

y - 2+ 2 = 4(x-3)+2

y = 4(x-3) + 2

Note that the equation is : y = 4(x-3) + 2

Now Distribute 4 to all terms within the parenthesis

y = 4(x-3) + 2

y = 4x - 12 + 2

Simplify. Combine like terms

y = 4x - 10 ; or f(x) = 4x - 10.

Hence, The linear function that represents the line giving by the point slope equation y-2=4(x-3) is f(x) = 4x - 10

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