Question 4 Unsaved
Henry places x marbles into an empty bucket. Each marble has the same weight. The weight, in ounces, of the bucket and marbles can be calculated using the expression shown.

3x + 8

What does the term 8 represent in this expression?

Question 4 options:

the weight of each marble


the weight of the empty bucket


the number of marbles


the total weight of the bucket and marbles

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.

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:

One marker would cost approx. $0.03

you answer is 5/8 please mark as brainliest if you need more help with questions like this lemme know

[tex]6r+5=11r\ \ \ \ |\text{subtract 6r from both sides}\\\\5=5r\ \ \ \ |\text{divide both sides by 5}\\\\\boxed{r=1}\\-------------------------\\\dfrac{2x-4}{2}=6x+3\\\\\dfrac{2x}{2}-\dfrac{4}{2}=6x+3\\\\x-2=6x+3\ \ \ \ \ |\text{add 2 to both sides}\\\\x=6x+5\ \ \ \ |\text{subtract 6x from both sides}\\\\-5x=5\ \ \ \ \ |\text{divide both sides by -5}\\\\\boxed{x=-1}[/tex]

least to greatest: -0.51, -1/2, 0.42, 11/20

greatest to least: 11/20, 0.42, -1/2, -0.51

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].

use the amount for each quantity to obtain theratio

choc chips : sugar = 5 : 3 = [tex]\frac{5}{3}[/tex]

Answer:

[tex]\frac{5}{3}[/tex]

Step-by-step explanation:

[tex]g(x)=\dfrac{x-1}{4}\to y=\dfrac{x-1}{4}\\\\\text{change x to y and y to x}\\\\x=\dfrac{y-1}{4}\ \ \ \ |\text{solve for y}\\\\\dfrac{y-1}{4}=x\ \ \ \ \ |\cdot4\\\\y-1=4x\ \ \ \ |+1\\\\y=4x+1\\\\\boxed{g^{-1}(x)=4x+1}[/tex]

[tex]f(x)=2x-5,\ g(x)=x^2-4x-8\\\\(f+g)(x)=f(x)+g(x)=(2x-5)+(x^2-4x-8)\\\\=2x-5+x^2-4x-8=x^2+(2x-4x)+(-5-8)=x^2-2x-13[/tex]

Answer:

[tex]\text{The value of (f+g)(x) is }x^2-2x-13[/tex]

Step-by-step explanation:

Given the two functions

[tex]f(x)=2x-5[/tex]

[tex]g(x)=x^2-4x-8[/tex]

we have to find the value of (f+g)(x)

As we know

[tex](f+g)(x)=f(x)+g(x)=(2x-5)+(x^2-4x-8)[/tex]

[tex]=2x-5+x^2-4x-8[/tex]

[tex]=x^2+2x-4x-5-8=x^2-2x-13[/tex]

[tex]\text{Hence, the value of (f+g)(x) is }x^2-2x-13[/tex]

the answer to your question :[tex]4\sqrt{5}[/tex]

hope this helps! ❤ from peachimin

Exact Form:√5

Decimal Form:2.23606797…

To solve an absolute value equation of the form |X| = k, where X is an expression with a variable and k is a non-negative number or an expression, you must solve the compound equation X = k or X = -k.

The first step is to divide both sides by 9 to get the absolute value of an expression equal to a non-negative number.

9|9 – 8x| = 2x + 3

Divide both sides by 9.

[tex] |9 - 8x| = \dfrac{2x + 3}{9} [/tex]

Now we eliminate the absolute value by rewriting this as a compound equation.

[tex] 9 - 8x = \dfrac{2x + 3}{9} ~~~or~~~ 9 - 8x = -\dfrac{2x + 3}{9} [/tex]

We must solve both equations.

Multiply both sides by 9.

[tex] 9(9 - 8x) = 2x + 3 ~~~or~~~ 9(9 - 8x) = -(2x + 3) [/tex]

[tex] 81 - 72x = 2x + 3 ~~~or~~~ 81 - 72x = -2x - 3 [/tex]

[tex] -74x = -78 ~~~or~~~ -70x = -84 [/tex]

[tex] x = \dfrac{-78}{-74} ~~~or~~~ x = \dfrac{-84}{-70} [/tex]

[tex] x = \dfrac{39}{37} ~~~or~~~ x = \dfrac{6}{5} [/tex]

Answer: x = 39/37 or x = 6/5

To check for extraneous solutions, we plug in each solution into the original equation and check if it works.

Check 39/37:

9|9 – 8(39/37)| = 2(39/37) + 3

|81 - 72(39/37)| = 78/37 + 3

|2997/37 - 2808/37| = 78/37 + 111/37

|189/37| = 189/37

189/37 = 189/37

The solution 39/37 is valid.

Check x = 6/5.

9|9 – 8x| = 2x + 3

9|9 – 8(6/5)| = 2(6/5) + 3

|81 - 72(6/5)| = 12/5 + 15/5

|405/5 - 432/5| = 27/5

|-27/5| = 27/5

27/5 = 27/5

The solution x = 6/5 is also valid.

There are no extraneous solutions.

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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The law of large numbers in probability, is a theorem that describes the result of performing the same experiment a large number of times because the average of the results obtained from a large number of trials is close enough to the expected value.

So, according to this definition and the situation given , the correct answer is option B - if 800 people are randomly surveyed about the TV shows they watch, about 400 of them will be women; because there are larger number of experiment.

Part B:

To get the expected value of a t-shirt we will multiply each of the 3 prices by the associated probability, and then add up these three products-

[tex](24\times\frac{1}{6})+(30\times\frac{1}{2})+(36\times\frac{1}{3})[/tex]

=4 + 15 + 12 = $31

Hence, option C is correct.

Answer:

1.  If 800 people are randomly surveyed about the TV shows they watch, about 400 of them will be women.

2. $31

Step-by-step explanation:

Got it right on the test.

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.

Learn more about forming equations here:

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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

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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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.

For more information about the probability

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[tex]E=\{-1,\ 0,\ 1,\ 2,\ 3,\ 4\}\\\\F=\{3,\ 4,\ 5,\ 6,\ 7,\ 8\}\\\\E\ \cup\ F=\{-1,\ 0,\ 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8\}[/tex]

All elements from set E and from the set F. The same elements are only once.

p = -4

q could be 6.5 units to the right   ...   or to the left   ...   of point p.

to the right: p + q   ⇒  [tex]-4 + (6\frac{1}{2}) = 2\frac{1}{2}[/tex]

to the left: p - q  ⇒ [tex]-4 - (6\frac{1}{2}) = -10\frac{1}{2}[/tex]

Answer: [tex]2\frac{1}{2}[/tex] or [tex]-10\frac{1}{2}[/tex]