Please help and show work!!

The domain and range of a function are sets of numbers that represent all possible inputs and outputs, respectively. They can be written using interval or set-builder notation, considering the function's definition and any restrictions. For instance, the domain [0, 20] implies the function is defined for any number between 0 and 20, inclusive.

Writing Out the Domain and Range of a Function

To write out the domain and range of a function, you first need to determine which values can be inputs (domain) and which can be outputs (range). The domain and range are written as sets of numbers, often in interval notation or set-builder notation. For instance, if a function f(x) is defined for all x such that 0 <= x <= 20, then its domain could be written as [0, 20].

The range is determined by evaluating the function at every value in its domain to find all possible outputs. For example, if f(x) = x^2 and x <= 0, the range would include all y <= 0 because squaring a non-positive number always yields a non-negative result. To restrict a function's domain and make it invertible, like the function y = x^2 restricted to x <= 0, one must consider which portions of the function pass the horizontal-line test.

For a function f(x) that is a simple relation, say f(x) = 2 for all x in its domain, the range is just {2} because no matter what x-value you put in, the output is always 2. In more complex functions, the graph may need to be analyzed to determine the exact range. When expressing domain and range, the domain is all valid inputs while the range is all possible outputs of the function.

Let the number of pages read on day 1 be = x

Then on day 2 he read twice the pages from day one, it is = 2x

On 3rd day he read 6 pages less than 1st day, it is = x-6

Total pages are = 458

The equation becomes: [tex]x+2x+x-6=458[/tex]

[tex]4x-6=458[/tex]

[tex]4x=464[/tex]

[tex]x=116[/tex]

So on the third day, Aiden read [tex]x-6=116-6=110[/tex] pages.

The number of pages Aiden read totals to the total number of pages of books. On the third day, Aiden read total 110 pages.

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For the given condition, for the missing value, we can use variables.

Since all the number of pages can be found if we'd have known the number of pages he read on the first day,  thus,

Let we take the number of pages Aiden read on the first day = P

Then, by the given condition, we get:

Number of pages Aiden read = twice the number of pages than he read on day one = [tex]2 \times P[/tex]

On third day = six pages less than what he read on first day = [tex]P - 6[/tex]

Since in these three days, he completed the whole book of 458 pages, thus, all these counts of pages he read in three days should total to 458. Or,

[tex]P + 2 \times P + P - 6 = 458\\4 \times P - 6 = 458\\\\\text{Adding 6 on both the sides and dividing by 4}\\\\\dfrac{4 \times P}{4} = \dfrac{458+6}{4}\\\\P = 116[/tex]

Thus, on the first day, Aiden read 116 pages.

Since on the third day, he read 6 pages less than the amount of pages he read on the first day, thus, number of pages he read on third day = 116 - 6 = 110

Thus, The number of pages Aiden read totals to the total number of pages of books. On the third day, Aiden read total 110 pages.

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the table below:

Grade        In favor   Opposed Undecided    Total

Grade 9     6                   4                       8                18

Grade 10     10         11                        9                30

Grade 11     12        15                      11                  38

Grade 12     15        6                      14                  35

If the principal randomly selects a student in grade 10 from this survey,

the probability that the student is opposed to extending the school day

P ( student in grade 10 is opposed)= Number of student in opposed(grade10) / total number of students in grade 10

Number of student opposed who is in grade10 = 11

total number of students in grade 10 = 30

P( student in grade 10 is opposed)=  [tex]\frac{11}{30}[/tex]

= 0.37

the probability that the student is opposed to extending the school day= 0.37

Final answer:

The probability that a randomly selected grade 10 student from the survey is opposed to extending the school day is 11/30, or approximately 36.67%.

Explanation:

The student's question pertains to the probability of selecting a grade 10 student who is opposed to extending the school day based on the survey results provided.

To calculate this probability, we consider only the grade 10 students. According to the table, there are 10 students in favor, 11 opposed, and 9 undecided within grade 10, making a total of 10 + 11 + 9 = 30 students surveyed in the tenth grade.

The probability that a randomly selected grade 10 student is opposed to an extended school day is the number of grade 10 students opposed divided by the total number of grade 10 students surveyed.

Mathematically, it can be represented as P(Opposed) = Number of opposed students in Grade 10 / Total number of students in Grade 10 surveyed. By plugging in the numbers:

P(Opposed) = 11 / 30

Therefore, the probability is 11/30 or approximately 0.3667, which can be expressed as a percentage by multiplying by 100, yielding about 36.67%.

Answer

Find out the how many rows will there be .

To proof

let us assume that the number of the rows will be x.

As given

There are 112 students in the Hammond Middle School marching band.

The band director wants students to march with 14 students in each row for the upcoming parade.

than the equation becomes in the form

[tex]x = \frac{112}{14}[/tex]

x = 8

Therefore the number of the rows will be 8.

Hence proved

Let cats = X

Then doges = 6x ( 6 times as many cats, so multiply 6 by number of cats)

Now you have X + 6X = 35  ( number of cats plus number of doags equal 35)

X +6x = 35

Simplify:

7X = 35

Divide both sides by 7 to solve for x:

X = 35 / 7

X = 5

Cats = X, so there are 5 cats.

Dogs = 6X = 6(5) = 30 total dogs.

multiplying by 0 will make the answer 0.

7 3/8(0) = 0

(7 3/8)x = 0

Answer:

The answer is 0 hope this helps

Step-by-step explanation:

P(A) = probability of event A, P(B) = probability of event B

P(A) = x is given to us

P(B) = y is also given

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

If A and B are independent, then neither event affects the other. If we know A happens, then that doesn't change the probability of B happening (vice versa).

So that means P(A|B) = P(A) = x and P(B|A) = P(B) = y

This points to the answer being P(B|A) = y which is choice A or the first answer choice

note: P(A|B) is read as "probability of A given that B has happened". It is known as conditional probability. The symbol between the A and B is not the letter i or L, it is a vertical pipe symbol to separate the letters.

Probability of independent events will be P(A/B) = P(A) = x and P(B/A) = P(B).

The probability of an event occurring is defined by probability.

Probability is also known as chance because, if you flip a coin, the likelihood that it will land on its head or tail is nothing more than the chance that either the head or the tail will occur.

In our daily time, there are several instances in the everyday world where we may need to draw conclusions about how everything will turn out.

The question is saying that event (A) and event (B) are independent it means

P(A/B) = P(A) is read by the probability of A after B events but for independent events, it doesn't matter.

P(B/A) = P(B) hence that will be the correct answer.

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-4 |x+5| = -16

Divide both sides by -4

|x+5| = 4

x = -1

[tex]-4|x + 5| = -16\\\\|x+5|=4\\\\x+5=4 \vee x+5=-4\\\\x=-1 \vee x=-9[/tex]

1 has the  greatest value in the number 1,567.

A number's place value is the worth of each digit. Depending on where it sits in a number, each digit has a varied value. The position of the digit in the number determines whether two similar digits in the same number have different values.

For example, the place value of 5 in 3458 is 5 tens, or 50. However, the place value of 5 in 5781 is expressed as 5 thousands or 5,000.

Given number:

1567

Now, keep looking the place value of each digit

7 - ones ---> 7x 1

6 - tens ---> 6 x 10

5 - hundred ---> 5 x 100

1 - thousand ---> 1x 1000

As, 1 has thousand place value.

Hence, 1 has the  greatest value in the number 1,567.

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The answer is:

                                    1919=2

Let us assume the numbers as follows:

9=1

8=2

1=0

6=4

2=0

Hence, when we substitute the assumed values in each of the given numbers we obtain the result for each as follows:

1)

9999=1+1+1+1

9999=4

2)

8888=2+2+2+2

8888=8

3)

1816=0+2+0+4

1816=6

4)

1212=0+0+0+0

i.e.

1212=0

5)

1919=0+1+0+1

i.e.

1919=2

Answer

The value of 1919 is 2

Explanation:  

Now find the value of 1919,

1 ⇒ 0

9 ⇒ 1

So, 1919 ⇔ 0101 ⇔ 0+1+0+1 = 2

Therefore, 1919 = 2

Further Explanation

Given, 9999= 4, 8888= 8, 8816= 6, 1212= 0,

If assume 9 as 1 for 9999 and add each 1 to get 4

So,  9999 ⇔ 1111 ⇔ 1+1+1+1 = 4

Therefore, 9 represents 1

If assume 8 as 2 for 8888 and add each 2 to get 8

So,  8888 ⇔ 2222 ⇔ 2+2+2+2 = 8

Therefore, 8 represents 2

If assume 1 as 0 and assume 6 as 2 for 8816 and add each digit to get 6

So,  8816 ⇔ 2202 ⇔ 2+2+0+2 = 6

Therefore, 1 represents 0 and 6 represents 2

If assume 2 as 0 for 1212 and add each digits to get 0

So,  1212 ⇔ 0000 ⇔ 0+0+0+0 = 0

Therefore, 2 represents 0

Learn More

Learn more about logical reasoning: https://brainly.com/question/8815372; Answered by:  Empathictruro

Keywords

Logical reasoning, high school mathematics, numbers, mathematical sum

Answer: D

Step-by-step explanation:

  y = x² + 16x + 70

-70                 -70

y - 70 = x² + 16x         next, complete the square by adding [tex](\frac{16}{2})^{2}[/tex] to both sides

y - 70 + 64 = x² + 16x + 64   remember that x² + 16x + 64 is a perfect square of (x - 8)²

y - 6 = (x + 8)²

   +6              +6

y      = (x + 8)² + 6

A: The other related equations would be:

K = °C + 273.15

K = °F + 457.87

Note: There are other equations that can be related, these are just ones that I find to be related. This is open to interpretation.

B:

23° C + 273.15 = 269.15 K

C:

300 K - 273.15 = 26.85 °C

300 Kelvins is greater than 25 degrees Celsius.

Given

ratio of elinor's age to his mother is 3 : 8

after 15 years

 the ratio will become 6:11

Find out the  elinor's age today and find her mothers age after 15 years.

To proof

As given in the question

ratio of elinor's age to his mother is 3 : 8

let x be the variable describe age.

let the elinor age = 3x

let the mother age = 8x

after 15 years

ratio will become 6:11

[tex]\frac{elinor\ age + 15 }{Mother\ age + 15 } = \frac{6}{11}[/tex]

As assume ealier elinor age be 3x and mother age be 8x

put this in the above equation

we get

[tex]\frac{3x + 15 }{8x + 15 } = \frac{6}{11}[/tex]

now sloving the above equation

we get

11 ( 3x + 15) = 6 ( 8x + 15 )

33x + 165 = 48x + 90

75 = 15x

[tex]x = \frac{75}{15}[/tex]

x = 5

Therefore

elinor's age today = 3x

                              = 3 × 5

                              = 15years

mothers age after 15 years = 8x + 15

                                              = 8× 5 + 15

                                              = 40 + 15

                                              = 55years

Hence proved

The problem is about solving a system of equations established from the given ratios of Elinor's and her mother's ages. Substitution method is used to find their present ages, and to find mother's age after 15 years, we add 15 to her current age.

This is a problem related to ratios and ages, which can be solved as an algebraic system of equations. Let's denote Elinor's present age as 'e' and her mother's age as 'm'. Then, from the problem we know that:

e/m = 3/8 (1), and

(e+15)/(m+15) = 6/11 (2).

From equation (1), we can express e as (3/8)m. We then substitute e in equation (2) to find the value of 'm'. Once we have 'm', we substitute its value in equation (1) to get 'e'. And to find her mother's age after 15 years, we add 15 to 'm'.

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2x² + 4x + 2

using long division to obtain the quotient

The result of dividing the polynomial 2x³ + 6x² + 6x + 2 by x + 1 is 2x² + 4x + 2, which can be obtained using synthetic division.

The given question is about polynomial division. To divide a polynomial, we commonly use long division or synthetic division. In this case, we are dividing the polynomial 2x³ + 6x² + 6x + 2 by (x + 1).

Using synthetic division, we get:

Therefore, the quotient is 2x² + 4x + 2.

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Answer:

The values of x are : [tex]2i[/tex] and [tex]-2i[/tex]

Step-by-step explanation:

Given equation is:   [tex]2x^2= -8[/tex]

First, we will divide both sides by 2 for getting rid of that 2 from the left side. So........

[tex]\frac{2x^2}{2}= \frac{-8}{2} \\ \\ x^2=-4[/tex]

Now, we need to take square root on both sides. So, we will get......

[tex]\sqrt{x^2}= \pm \sqrt{-4} \\ \\ x=\pm \sqrt{4(-1)} \\ \\ x=\pm 2\sqrt{-1}= \pm 2i[/tex]

(Replacing [tex]\sqrt{-1}[/tex] as  [tex]i[/tex] )

So, the solutions are: [tex]x= 2i, -2i[/tex]

Answer:

2i or -2i

Step-by-step explanation:

Answer:

Number of miles he walks in 1 hour = [tex]\frac{10}{x}[/tex].

Step-by-step explanation:

If a man walks 10 miles in x hours, we need to find how many miles he walks in 1 hour.

Number of miles the man walks can be found by dividing 10 miles by x hours.

Therefore,

Number of miles he walks in 1 hour = [tex]\frac{10}{x}[/tex].

[tex]Q6.\\v(x)=x^2-20\\\\v(x+4)=(x+4)^2-20=x^2+2(x)(4)+4^2-20\\=x^2+8x+16-20=x^2+8x-4[/tex]

[tex]TRUE[/tex]

[tex]Q7.\\c(x)=5x^2+12x,\ d(x)=7x+5x^2\\\\c(x)-d(x)=(5x^2+12x)-(7x+5x^2)=5x^2+12x-7x-5x^2\\\\=(5x^2-5x^2)+(12x-7x)=5x[/tex]

[tex]Q8.\\f(x)=6x+1,\ f(a)=25\\\\f(a)=6a+1\\\\\text{substitute}\\\\6a+1=25\qquad|-1\\\\6a=24\qquad|:6\\\\a=4[/tex]

The correct answer is a = 4

Hello...

A plumber charges $55 per hour plus a $50 service charge. Kevin hired the plumber to install a new hot water heater. What are the total charges if the plumber took 4 hours to complete the installation? A. $220 B. $250 C. $255 D. $270

We Know:

$55 per hour

$50 Service Charge

Plumber took 4 hours

Find:

The total cost

Solution:

55 x 4 = 220

220 + 50 = 270

Answer:

Total Cost - $270

Answer:

[tex]\dfrac{1}{3,357,900}[/tex]

Step-by-step explanation:

There are

[tex]C^{42}_4=\dfrac{42!}{4!(42-4)!}=\dfrac{42!}{4!\cdot 38!}=\dfrac{38!\cdot 39\cdot 40\cdot 41\cdot 42}{2\cdot 3\cdot 4\cdot 38!}=39\cdot 10\cdot 41\cdot 7=111,930[/tex]

different ways to select the  four numbers between 1 and 42. Only one of this ways is correct (successful to win).

There are 30 different ways select the single number between 1 and 30. Only one of them is correct.

The  probability of winning the jackpot is

[tex]\dfrac{1}{111,930}\cdot \dfrac{1}{30}=\dfrac{1}{3,357,900}[/tex]

The probability of winning the jackpot in the particular lottery is 1 in 9,335,082,240.

To find the probability of winning the jackpot, we need to calculate the probability of selecting the correct four numbers between 1 and 42 and the correct single number between 1 and 30.

For the four numbers, the probability of choosing each number correctly is 1/42 since there are 42 numbers to choose from and only one is correct. Since the selections are independent, we can multiply the probabilities together to get the overall probability of choosing all four numbers correctly: (1/42) * (1/42) * (1/42) * (1/42) = 1/311,169,408.

For the single number, the probability is 1/30 since there are 30 numbers to choose from and only one is correct.

To find the overall probability of winning the jackpot, we multiply the probabilities of selecting the four numbers correctly and the single number correctly: (1/311,169,408) * (1/30) = 1/9,335,082,240.

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Hey there!!

Given :

g(x) = ax² + 24

and

g(4) = 8

g(4) = a(4)² +24

g(4) = 16a + 24

8 = 16a + 24

-16 = 16a

a = -1

The constant is -1.

g(-4) =?

g(-4) = -1(-4)² + 24

g(-4)  = -16 + 24

g(-4) = 8

The answer is (A)

Hope it helps!