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The mistake made by the student was using the composition f ° g(x) instead of g ° f(x). The correct form is g( f(0)) = - 9 / 2.

In this question we find two functions, with which we should perform an operation known as composition. Composition consists in substituting the input of a function by the other function. The operation is defined by the following expression:

f ° g (x) = f [g (x)]

Herein we must determine the mistake done by the student on the composition. If we know that f(x) = (3 · x - 7) / 4, g(x) = 2 · x - 1 and x = 0, then the value of g(f (0)) is:

g ° f (x) = g (f (x))

g ° f (x) = 2 · [(3 · x - 7) / 4]  - 1

g ° f (x) = (3 · x - 7) / 2 - 1

g ° f(x) = (3 / 2) · x - 7 / 2 - 1

g ° f(x) = (3 / 2) · x - 9 / 2

g ° f(0) = (3 / 2) · 0 - 9 / 2

g ° f(0) = - 9 / 2

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Answer:   Product of extremes (numbers on extreme edges) = product of means i.e., ad = bc

a, b, c, d,…. are in continued proportion means, a:b = b:c = c:d

a:b = b:c then b is called mean proportional and b2 = ac

The third proportional of two numbers, a and b, is c, such that, a:b = b:c

d is fourth proportional to numbers a, b, c if a:b = c:d

Step-by-step explanation:

Answer: GoodMorning: ) ✨ According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol '::' or '='. For example, 2:5 :: 4:8 or 2/5 = 4/8.

Two values x and y are said to be directly proportional to each other when the ratio x:y always remains the same. Example : If we buy two pen for 50 Rs. It will cost us 100 Rs for four pen. Two values x and y are said to be inversely proportional to each other when the ratio x:y1 always remains the same.

Hope This Helps <3

Step-by-step explanation:

Answer: The least common denominator (LCD) is 1015.

The key features of the function are

The function is given as

f(x) = |x - 3|

The above function is an absolute value function, and the key feature are:

Generally, the domain of an absolute value function is the set of all real values

This means that

Domain: -∝ < x < ∝

An absolute value function is represented as

f(x) = a|x - h| + k

Where

Vertex = (h, k)

By comparison, we have

Vertex = (3, 0)

a = 1

Because the variable a is positive, the vertex of the function is a minimum

So, the range is [0, ∝)

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Answer:

can you respond and explain more

Step-by-step explanation:

Answer:

One angle is 70 and the other angle is 110

Step-by-step explanation:

x + 40 = y

x + y = 180  Supplemental angles add to 180

Substitutes x + 40 into the second equation by y

x + x + 40 = 180  Combine like terms

2x + 40 = 180  Subtract 40 from both sides

2x = 140  Divide both sides by 2

x = 70

Substitute in 70 for x in either of the original 2 equations

x + y = 180

70 + y = 180  Subtract 70 from both sides

y = 110

m1=70

m2=110

supplementary angles are two angles that add up to 180 so all you need to do is make an equation to find the answer.

we can make m1=x and m2 = y

x is less than y by 40 degrees so y-40=x

then we use the equation x+y=180 and replace x with what we found out and solve for y.

(y-40)+y=180 ---> 2y -40 = 180 ---> 2y = 220 ---> y=110

x+y=180 ---> x+110=180 ---> x=70

Answer:

56

Step-by-step explanation:

1/2 x 14 x 8

use the formula: half times base times height

the range of the graphed relation is just:

R: y ∈ {2, 3, 4, 5, 6}

A relation maps elements x into elements y, and for that relation, we define the domain as the set of the possible inputs (values of x) and the range as the set of outputs (set of values of y).

On the table you already wrote we can see that the values of y are:

2, 3, 4, 5, 6

Then the range is just:

R: y ∈ {2, 3, 4, 5, 6}

Where "∈" means "belongs".

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The number of particles which are in 12 moles of any substance given the premise that; 1 mole contains 6.02×1023 particles is; 7.224 × 10²³.

It follows from the task content that 1 mole contains 6.02×1023 particles, and hence, the number of particles in 12 moles is to be determined.

On this note, it follows from proportion that since 1 mole contains 6.02×1023 particles, then, the number of particles is 12 moles is;

= 12 × 6.02 × 10²³

= 72. 24 × 10²³

= 7.224 × 10²³.

Ultimately, The number of particles which are in 12 moles of any substance given the premise that; 1 mole contains 6.02×1023 particles is; 7.224 × 10²³.

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Based on the amount that Tim had at the beginning of the month, the mowing of the lawn and washing of the car, the equation that represents the situation is b. 50 + 12 + 12 + 9 + (-15) + (-15) + (-35).

The amount of money that Time has left is $18

Tim gets $12 for every lawn he mows and $9 for every car he washes.

The amount he gets is:
= Amount started with + payment for mowing lawn + payment for mowing another lawn + payment for car wash

= 50 + 12 + 12 + 9

When the expenses of the video games and sweatshirt are thrown in, the formula becomes:

=  50 + 12 + 12 + 9 + (-15) + (-15) + (-35)

The amount that Tim is left with is:

= 50 + 12 + 12 + 9 + (-15) + (-15) + (-35)

= $18

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Answer:

5 7/9

Step-by-step explanation:

3 2/3 + 2 1/9 get the common denominator of 9 by making 2/3 6/9

3 6/9 + 2 1/9 add whole numbers to get 5 and numerators to get 7/9

thus 5 7/9

hope this helps! :)

Answer:

I want to say you have a 6/24 chance.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The total number of CD is given as:  24

Answer:

7y

Step-by-step explanation:

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

2x + 3y - 2x + 4y

2x - 2x + 3y + 4y

3y + 4y

7y

*Please mark brainliest answer

The transformations that occurred to g(x) are horizontal stretch by a factor of 4 and a down translation by 4 units

The equation of the functions are given as

f(x)= (4x - 8)^2

g(x) = x^2

Start by stretching the function g(x) horizontally by a scale factor of 4

This is represented as

g'(x) = g(4x)

So, we have

g(4x) = (4x)^2

This gives

g'(x) = (4x)^2

Next, we translate the function down by 8 units

This is represented as

f(x) = g'(x - 8)

So, we have

f(x) = (4x - 8)^2

Hence, the transformations that occurred to g(x) are horizontal stretch by a factor of 4 and a down translation by 4 units

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When the the mean height of the 14 boys is 1.56 meters and the mean of all students is 1.515 meters then the mean height for the girls will be 1.48.

From the question, we were given total number of students as  32

But the mean can be calculated as the ratio of all the sum of all the data to the total number of data,

the total height of all students= (32*1.56)=48.48

total height of 14 boys=(14*1.56)=26.64

number of girls is (32-14)=18

The mean height for the girls will be (26.64/1118)=1.48

Therefore, When the the mean height of the 14 boys is 1.56 meters and the mean of all students is 1.515 meters then the mean height for the girls will be 1.48.

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NOTE; This is a complete question , no given option , even on internet.

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{6}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 7 -5}{2}~~~ ,~~~ \cfrac{ 6 -4}{2} \right) \implies \left(\cfrac{ 2 }{2}~~~ ,~~~ \cfrac{ 2 }{2} \right)\implies (1~~,~~1)[/tex]

The number of fliers that he has not posted is 8

Proportion can be defined as the mathematical comparison of two elements or numbers.

From the information given, we have that;

To determine the number of fliers remaining, we have that;

Remaining fliers for the First week

= 84 × 1/6

Multiply and find the quotient

= 14 fliers

Fliers remaining after the last week

= 14 × 4/7

Multiply and find the quotient

= 56/7

= 8 fliers

Thus, the number of fliers the he has not posted is 8

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Answer: $20 per hour

Step-by-step explanation:

To find the hourly rate, simply divide the total cost by the amount of hours that the object was rented(same for unit price).

160/8=20

The hourly rate for the bounce house rental is $20.

The linear inequality for the statement " the sum of a number and 17.3 is at least −2.8" is  b + 17.3 ≥ - 2.8 which is option B

We are given that the sum of a number and 17.3 is at least −2.8 and we have to form a linear inequality from the information provided

Let the number be b

so, the sum of two numbers would be

b + 17.3

It is given that the sum should be at least - 2.8

this means the sum is either equal to - 2.8 or sum is more than -2.8

So, the linear inequality equation comes to be

b + 17.3 ≥ - 2.8

Hence, the linear inequality for the statement " the sum of a number and 17.3 is at least −2.8" is  b + 17.3 ≥ - 2.8 which is option B

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Answer:

b

Step-by-step explanation:

gimmeeeeee 10000 pointttsss.

The circled graph given at the end of the answer is not a function of x.

The graphs for which we choose the one which is not a function are missing, and are given at the end of the answer.

A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y. Vertically aligned points mean that a value of x is mapped to multiple values of y, that is, a single input is mapped to multiple outputs which disqualify the relation as a function.

For this problem, we have that:

Hence the circled graph given at the end of the answer is not a function of x.

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Answer:

Step-by-step explanation:

Answer:

1) y=160+0.5x

2) 210 miles=x

Answer:

5

Step-by-step explanation:

First we'd need to solve 5 x 6. When we solve 5 x 6 we'd get the answer 30. Then do 7 - 3, when we solve that we'd get the answer of 4. Now we add 4 with 2 and we'd get 6. Now we get the 30 and divide it with 6 and get our answer as 5. Therefore our final answer is 5.

I hope this helps, have a blessed day! :)

Find the negative reciprocal of the slope of the original line and use the point-slope formula y-y_(1)=m(x-x_(1)) to find the line perpendicular to y(1)/(2)x-5.

y=-2x-5

Step-by-step explanation:

New data point is residual.

When a data point is added or removed from the whole dataset, it might cause a significant change in the regression equation by either changing the slope or the relationship coefficient existing between the variables.

An influential point is one that changes the relationship existing between the dependent and the independent variables significantly in either direction.

Since the new observed data point decreases the slope of the regression line but increases the correlation coefficient existing between the independent and the dependent variable, we can probably say that the new data point is an influential point.

Thus, Option B. is correct.

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Answer:

Good

Step-by-step explanation:

it is a

Answer:2400 miles

Step-by-step explanation:

150 miles in 1/2 hour. 150x2=300. 300 miles in 1 hour.300x8=2400. 2400 miles in 8 hours.

Answer:

Yes.

Step-by-step explanation:

-5 3/11 is equal to -5.27 repeating therefore, it is greater than -5.2. Hope this helps. :)

It is important to have C=200 pounds of empty cans, which is the amount of weight in pounds that the class needs to collect.

This is further explained below.

Generally, the equation for empty cans is  mathematically given as

C= books total cost/ current price

Therefore

[tex]C=\frac{50}{(\frac{1}{4})}[/tex]

C= 200

In conclusion, the pounds of empty cans the class has to collect is

C=200 pounds are needed.

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