Arrange the functions in ascending order, starting with the function that eventually has the lowest value and ending with the function that eventually has the greatest value.
2x+5
2^x+3
2^x+10
2x
x²+2
x²
PLEASE HELP 20 POINTS PROVIDED

total was 49.10

mileage would be 49.10 = 2.10x +5.00

 total miles =

49.10 = 2.10 +5.00

44.10 = 2.10x

x = 44.10/2.10 = 21 miles

The equations to solve for [tex]\( |2x-3|=x+6 \)[/tex] are [tex]\( 2x - 3 = x + 6 \)[/tex] and [tex]\( 2x - 3 = -(x + 6) \).[/tex]

Let's solve the absolute value equation |2x-3|=x+6 step by step.

We'll start by writing down the equation:

|2x - 3| = x + 6

Since the absolute value expression |2x - 3| can be either positive or negative, we'll split the equation into two cases:

  Case 1: 2x - 3 = x + 6

  Case 2: 2x - 3 = -(x + 6)

Let's solve Case 1:

  2x - 3 = x + 6

  Subtract x from both sides:

  2x - x - 3 = 6

  Simplify:

  x - 3 = 6

  Add 3 to both sides:

  x = 9

Now, let's solve Case 2:

  2x - 3 = -(x + 6)

  Distribute the negative sign:

  2x - 3 = -x - 6

  Add x to both sides:

  2x + x - 3 = -6

  Simplify:

  3x - 3 = -6

  Add 3 to both sides:

  3x = -3  

  Divide both sides by 3:

  x = -1

So, the solutions to the equation |2x-3|=x+6 are x = 9 and x = -1.

Answer:

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power, as 1385.62 written as [tex]1.3862*10^{4}[/tex].

Step-by-step explanation:

Answer:

D. [tex](x-6)(x+2)[/tex]

Step-by-step explanation:

We have been given a polynomial [tex]x^2-4x-12[/tex]. We are asked to find the factors of our given polynomial.

We will use splitting the middle term format of factoring quadratic polynomial.

We need two numbers, whose product is [tex]-12[/tex] and whose sum is [tex]-4[/tex]. Such two numbers are  [tex]-6\text{ and }2[/tex].

[tex]x^2-6x+2x-12[/tex]

[tex](x^2-6x)+(2x-12)[/tex]

Factor out GCF of each group:

[tex]x(x-6)+2(x-6)[/tex]

[tex](x-6)(x+2)[/tex]

Therefore, factors of our given expression are [tex](x-6)(x+2)[/tex] and option D is the correct choice.

The correct option is A. [tex]m=-4[/tex]. By substituting the second equation into the first one in the system of equations, the value of m is -4.

The value of m in the system of equations can be found by substitution or elimination. Starting with the given equations:

[tex]m - 2n = 8 (1)[/tex]

[tex]n = m - 2 (2)[/tex]

Using the second equation (2) to substitute for n in the first equation (1):

[tex]m - 2(m - 2) = 8[/tex]

[tex]m - 2m + 4 = 8[/tex]

[tex]-m + 4 = 8[/tex]

[tex]-m = 8 - 4[/tex]

[tex]-m = 4[/tex]

[tex]m = -4[/tex]

This means that the value of m is -4, which corresponds to option A.

A functions B and D are valid functions because they meet the criteria of each x value having only one corresponding y value.

Function B: You mentioned that B is a function because each x value has only one corresponding y value. In mathematical terms, a function is defined as a relation between a set of inputs (x values) and a set of outputs (y values), where each input (x) maps to exactly one output (y). So, if B satisfies this definition, it is indeed a function.

Function D: Similar to B, if D also adheres to the definition of a function, where each x value corresponds to only one y value, then it is a function as well.

Function A: You mentioned that for A, the x value of 1 has 2 y values. In mathematical terms, a function cannot have one input (x) mapping to multiple outputs (y). If this is the case for A, it does not meet the definition of a function.

Function C: You mentioned that for C, the x value of 7 has 2 y values, 10 and 3. Again, if one input (x) is associated with multiple outputs (y) in C, it does not qualify as a function.

In summary, functions B and D are valid functions because they meet the criteria of each x value having only one corresponding y value. Functions A and C do not meet this criterion and are not functions in the mathematical sense.

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For the given probabilities P(A∩B) = 1150 and P(A|B) = 1120, using Bayes' theorem for conditional probability, the probability of event B, P(B), is found to be approximately 1.027.

The topic of this question is probability, specifically concurrent events in probability theory. Here, we use Bayes' theorem for conditional probability which states that P(A|B) = P(A ∩ B) / P(B).

Given that P(A∩B) = 1150 and P(A|B) = 1120, we can plug these values into the formula to find P(B). Hence, P(B) = P(A ∩ B) / P(A|B), substituting the given numbers, we get P(B) = 1150 / 1120 = 1.027 approximately.

So P(B), the probability of event B occurring, we would expect to be approximately 1.027 (or 102.7% assuming the probabilities were in decimal form to start with).

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Alright, let's solve the problem with these given values.

The formula for calculating the probability of B in the context of A and B both happening is:

`P(A and B) / P(A|B)`.

In this case, the probability of A and B occurring is 1150, while the likelihood of A given that B has occurred is 1120. We can substitute these values into the formula:

So, P(B) = P(A and B) / P(A|B)

Substitute the given into the formula:

P(B) = 1150 / 1120 = 1.0267857142857142

Therefore, the Probability of event B (P(B)) is approximately 1.027 when rounded to three decimal places.

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Answer:

The given statement is true.

Step-by-step explanation:

We have been given a statement and we are supposed to determine whether our given statement is even or odd.

Statement: The sine function is an odd function.

We know that sine is symmetric about origin and [tex]\text{sin}(-x)=-\text{sin}(x)[/tex]. Therefore, sine is an odd function and our given statement is true.

Answer:

The answer is [tex]Income=100*r+40*b[/tex]

Step-by-step explanation:

In this case we have to construct an expression that describe the income of selling the rocking chairs ($100 each - r) and the bar stool ($40 each - b), so the total income will depend on the addition of this two variables multiplied by its individual price, this is:

[tex]Income=100*r+40*b[/tex]

The answer is [tex]Income=100*r+40*b[/tex]

The best statement which is true for the graph y=-2x is that Yes, the points shown on the line would be a part of y=-2x.

A line is collection of various points on a surface which together joins two points on a surface. Equation of a line looks like y=a +b x where b is the slope of line.

We have been given an equation y=-2x and we have to find the graph of equation and for that we need to find points and for this we have to put the values of x which gives the values of y.

At x=0 ,y=0

At x=1 ,y=-2*1=-2

At x=2  ,y=-2*2=-4

At x=-1 ,y=-2*-1=2

Coordinates will be (0,0),(1,-2),(2,-4),(-1,2)

If we find these points on this line then will surely be able to find these points.

Hence the statement which is true is that Yes, the points shown on the line would be part of y = −2x.

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I’ve answered this before so here’s the complete given for this problem.

Danielle conducts an experiment by tossing a fair coin three times. She records the number of heads out of the three trials. The probabilities are given in the table below (X = number of heads out of three trials). 

Given:

x 0 1 2 3 
P(x)1/8 3/8 3/8 1/8 


 n = 3; p = 0.5; q = 0.5; P(x = 0) = nCx p^x 
x N(x) P(x) ΣP(x) 1- ΣP(x) x * P(x) 
--- ----- --------- --------- --------- --------- 
0 1 0.125 0.125 0.875 0 
1 3 0.375 0.5 0.5 0.375 
2 3 0.375 0.875 0.125 0.75 
3 1 0.125 1 0 0.375 

0+.375+.75+.375 = 1.5

         The answer is:

Sigma 960 (1/4)^i-1 ;    the sum is 1280

We are given the first term of the geometric sequence as:

[tex]a_1=960[/tex]

Also, the common ratio of the terms in geometric sequence is: [tex]\dfrac{1}{4}[/tex]

We know that if the series is a geometric series than the sum of the terms is given by:

[tex]a+ar+ar^2+.....\\\\=a(1+r+r^2+....)\\\\=\sum ar^{n-1}[/tex]

where a is the first term of the series and r is the common difference.

Here a=960

and r=1/4

Hence,

The sum of the series is:

[tex]=\sum 960(\dfrac{1}{4})^{i-1}[/tex]

Now we know that the sum of the infinite geometric series is given by:

[tex]S=\dfrac{a}{1-r}[/tex]

where S is the sum of the series.

Hence, here the sum of the series is calculated by:

[tex]S=\dfrac{960}{1-\dfrac{1}{4}}\\\\\\S=\dfrac{960}{\dfrac{3}{4}}\\\\\\S=\dfrac{960\times 4}{3}\\\\\\S=1280[/tex]

Hence, the sum is:   1280