The mapping diagram shows a functional relationship.
Complete the statement.
f(3) is
Domain
Range
0
3
Tomos
-1
9
9

Answer:

\(x=2\\x=-\frac{1}{2}\)

Step-by-step explanation:

1) Move terms to the left side.

\(3x=2x^{2} -2\\3x-(2x^{2}-2)=0\)

2) Distribute.

\(3x-(2x^{2} -2)=0\\3x-2x^{2} +2=0\)

3) Rearrange terms.

\(3x-2x^{2} +2=0\\-2x^{2} +3x+2=0\)

4) Common factor.

\(-2x^{2} +3x+2=0\\-(2x^{2} -3x-2)=0\)

5) Divide both sides of the equation by the same term.

\(-(2x^{2} -3x-2)=0\\2x^{2} -3x-2=0\)

6) Use the quadratic formula.

\(x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}\)

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

\(2x^{2} -3x-2=0\\a=2\\b=-3\\c=-2\)

\(x=\frac{-(-3)+\sqrt{(-3)^{2} -4*2(-2)} }{2*2}\)

7) Simplify.

Evaluate the exponent

\(x=\frac{3+\sqrt{(-3)^{2}-4*2(-2) } }{2*2}\)

\(x=\frac{3+\sqrt{9-4*2(-2)} }{2*2}\)

Multiply the numbers

\(x=\frac{3+\sqrt{9-4*2(-2)} }{2*2}\)

\(x=\frac{3+\sqrt{9+16} }{2*2}\)

Add the numbers

\(x=\frac{3+\sqrt{9+16} }{2*2}\)

\(x=\frac{3+\sqrt{25} }{2*2}\)

Evaluate the square root

\(x=\frac{3+\sqrt{25} }{2*2} \\x=\frac{3+5}{2*2}\)

Multiply the numbers

\(x=\frac{3+5}{2*2}\)

\(x=\frac{3+5}{4}\)

8) Seperate the equations.

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

\(x=\frac{3+5}{4}\)

\(x=\frac{3-5}{4}\)

9) Solve.

Rearrange and isolate the variable to find each solution.

\(x=2\\x=-\frac{1}{2}\)

The probability that a rises and b does not rise in price is: 24%

We can use conditional probability to solve this problem.

Let A = "fund a rises in price" and B = "fund b rises in price".

From the information provided, we know that:

Using the formula for conditional probability, we can find the probability that a occurs and b does not occur:

We don't know the probability of a, but we can find it using the formula for conditional probability and Bayes' theorem:

Substituting in the known probabilities:

Solving for P(A), we get:

Now we can use this value to find P(A and B'):

So, the probability that fund a rises in price and fund b does not rise in price is 0.24 or 24%.

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The variance of the sample means that is found in the sample distribution that we have here is 0.3333

This is the measure of dispersion that is used to show the spread of the data that is contained in a data set

The formula that we are to use here is given as

b² - a² / b - a

we have to put the values in this question

(14 - 2)² / 14 - 2

= 144 / 12

= 12

From here we would have to solve for the variance.

The variance = 12 / 35

= 0.3333

Hence the variance that we have in the question is equal to 0.3333

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Solution

A pair of dice rolled has a total of 36 possible outcomes

The number of two 4's = 1

An expression for the probability is

No of required events = 1

Total no of possible events

Answer:

512 inches cubed

Step-by-step explanation:

8^3 is equal to 512

Answer:

512 inches

Step-by-step explanation:

8^3 = 8*8*8 = 64*8 = 512 inches

Answer:

35

Step-by-step explanation:

I used Symbolab here's the screenshot

The​ p-value is the probability of getting a test statistic at least as extreme as the one representing the sample​ data, assuming that the null hypothesis is true.

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The equation relating x, y, and z is:

z = 0.5 * x * y.

In the given problem, the relationship between x, y, and z can be expressed by the equation z = k * x * y, where k represents the constant of proportionality. By substituting the values of x = 4 and y = 5, when z is equal to 10, we can determine the value of the constant of proportionality, k, and further define the relationship between the variables.

To find the constant of proportionality, we substitute the known values of x = 4, y = 5, and z = 10 into the equation z = k * x * y. This gives us the equation 10 = k * 4 * 5. By simplifying the equation, we have 10 = 20k. To isolate k, we divide both sides of the equation by 20, resulting in k = 0.5. Therefore, the equation relating x, y, and z is z = 0.5 * x * y, meaning that z is directly proportional to the product of x and y with a constant of proportionality equal to 0.5.

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Answer: 5:12< 7:9

Step-by-step explanation: (5:12) x3=   15:36  <  21:36  (7:9)x3=21:36

Answer:

\(\frac{5}{12} < \frac{7}{9}\)

Step-by-step explanation:

\(5:12\)  \(7:9\)

\(5*9\)  \(7*12\) (using cross multiply)

\(45 < 84\)

Therefore your answer is \(\frac{5}{12} < \frac{7}{9}\)

Extra:

I hope this helped at all.

Note: (Please don't delete this answer moderators.)

If the outside temperature over a day can be modeled as a sinusoidal function and if the high temperature for the day is 80 degrees and the low temperature of 40 degrees occurs at 3 AM, assuming t is the number of hours since midnight, then an equation for the temperature, D, in terms of t is D = 20*sin(π/12(t-3)) + 60.

To find the equation, follow these steps:

Thus the equation for the temperature, D, in terms of t is D = 20sin(π/12(t-3)) + 60

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Answer:

first option is easiest since it involves just adding both equations term by term.

3m+n=71

2m-n=30

Step-by-step explanation:

The first system looks like the easiest one, because the two equations are listed already in standard form, and the variable "n" appears as positive "n" in the first equation, and as its opposite "-n" in the second equation. Therefore the elimination method works directly by adding both equations term by term (thus cancelling out completely one of the variables in the resultant/combined equation.

Answer:

24 packages

Step-by-step explanation:

Given

Represent Napkins with N and Cups with C

\(C = 8's\)

\(N = 12's\)

Required

Determine the smallest amount of N and C that will be equal

To do this, we simply calculate the LCM of N and C as follows:

List out the multiples of each..

\(C = 8,16,24,30....\)

\(N = 12,24,36,48...\)

The common multiple between both is 24.

Hence, 24 packages of N and C answers the question

Answer:

6 hours without exceeding

Step-by-step explanation:

7 hours goes over

100+40x7=380

6 hours is under

100+40x6=340

Answer:

The vertex.

Step-by-step explanation:

Step-by-step explanation:

X=7 or x=5

It might be two answer to this question

\(\huge\textsf{Hey there!}\)

\(\large\textsf{(x - 7) (x - 5)}\)

\(\large\text{DISTRIBUTE each of the numbers}\)

\(\large\textsf{x(x) + (-5)x + (-7(x) + (-7)(-5)}\)

\(\large\textsf{x(x) = \bf x}\bf ^2\)

\(\large\textsf{x(-5) = \bf -5x}\)

\(\large\textsf{-7(x) = \bf -7x}\)

\(\large\textsf{(-7)(-5) = \bf 35}\)

\(\mathsf{x^2 - 5x -7x + 35}\)

\(\large\text{COMBINE the LIKE TERMS}\)

\(\mathsf{x^2 -(5x - 7x) + 35}\)

\(\mathsf{-5x -7x = \bf -12x}\)

\(\mathsf{x^2 - 12x + 35}\)

\(\boxed{\huge\text{Answer: \bf x}^2 \huge\text{\bf - 12x + 35}}\huge\checkmark\)

\(\large\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitirite1040:)}\)

Answer:

Here's your answer

Hope it helps!!

Answer:

watch a video or use a hint.

Step-by-step explanation:

it say it.

The solution of the given recurrence relation `T(n) = 2T(n/2) + 23n` using all three methods are:`T(n) = Θ(nlog2n)`

Given recursive relation is `T(n) = 2T(n/2) + 23n`.

We have to solve the above recursion using all three methods in any order we choose and label each solution as recursion tree, substitution, or Master Theorem.

Now, let's solve the above recursion using all three methods one by one:

1. Recursion Tree method:

To solve the above relation using recursion tree method, we will create a tree and the value of each level will be the sum of the values of all nodes present in that level or the sum of all previous levels + current level.

The tree will look like:

Therefore, the answer of the given recurrence relation `T(n) = 2T(n/2) + 23n` using the recursion tree method is:

`T(n) = Θ(nlog2n)`

2. Substitution method:

To solve the above recurrence relation using the substitution method, we can assume a solution and prove it by the Mathematical induction method.

Let `T(n) = 2T(n/2) + 23n`

Then, `T(n/2) = 2T(n/4) + 23n/2`

Also, `T(n/4) = 2T(n/8) + 23n/4`

Therefore, `T(n) = 2(2T(n/4) + 23n/2) + 23n`Or, `T(n) = 2²T(n/2²) + 23n(1 + 2)`

In general, we have `T(n) = 2kT(n/2k) + 23n(1 + 2 + ... + 2k-1)`

When `n/2k = 1`Or, `k = log2n`

Therefore, `T(n) = 2log2nT(1) + 23n(1 + 2 + ... + 2log2n-1)`Or, `T(n) = 2log2nT(1) + 23n(2log2n - 1)`

As `T(1) = 1`

Therefore, `T(n) = Θ(nlog2n)`

Hence, the answer of the given recurrence relation `T(n) = 2T(n/2) + 23n` using the substitution method is:

`T(n) = Θ(nlog2n)`

3. Master Theorem method:

To solve the above recurrence relation using the Master theorem, we have to compare the function `nlogba` with the function `f(n)`.

Here, `a = 2`, `b = 2`, and `f(n) = 23n`.

As per the Master theorem:

`If f(n) = Θ(nlogba),

then T(n) = Θ(nlogba log2n)` `

               = Θ(nlog2n)` if

`f(n) = 23n

      = Θ(nlog2n)`

Therefore, the solution of the given recurrence relation `T(n) = 2T(n/2) + 23n` using the Master theorem is:

`T(n) = Θ(nlog2n)`

Hence, the solution of the given recurrence relation `T(n) = 2T(n/2) + 23n` using all three methods are:`T(n) = Θ(nlog2n)`

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To establish the existence of a causal relationship between the thickness of the packaging material and the shelf life of the cheese,

In a dairy factory, the best study that would be a reliable source of evidence is a randomized controlled trial (RCT).In an RCT, the participants are randomly assigned to two or more groups,

where one group receives the intervention (in this case, cheese packaged with thicker material) and the other group receives the standard treatment (cheese packaged with the usual material).

To ensure the reliability of the study, the RCT should be conducted in a double-blind manner, where neither the participants nor the researchers know which group is receiving the intervention. This will prevent any bias that may influence the results.

The participants should also be selected carefully to ensure that they represent the target population of the study. In this case, the participants should be cheese consumers or distributors who are interested in the shelf life of the cheese.

By comparing the shelf life of the cheese packaged with thicker material to that packaged with the usual material, the RCT can establish the existence of a causal relationship between the thickness of the packaging material and the shelf life of the cheese.

The results of the study can then be used to inform the dairy factory's packaging practices and improve the shelf life of their cheeses.

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Answer: Positive correlation

Step-by-step explanation:

As you go up and along the graph the values go up.

Both have to be increasing basically.

Answer:

16: 24ab, a negative times a negative always makes a positive by the way

17: 6x^4

18: 15, 15-8=7, then 7x3=21

19: -2x+8

20: 8a

21: y x y x y

22: 2a+3b

23: 6a^4

24: x times x times x times x

25: 49y^2

The rational function for this problem is defined as follows:

A. F(x) = 1/[(x + 1)(x + 5)]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator, hence they are given as follows:

x = 1 and x = 5.

Hence the denominator is given as follows:

(x - 1)(x - 5).

The function has no intercepts, hence the numerator is a constant.

Thus the function is given as follows:

A. F(x) = 1/[(x + 1)(x + 5)]

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Answer:

it should be 9 because 12÷6 givss you 2 so 54÷6 gives you 9

Answer:

$541

Step-by-step explanation:

1). $550 - $120 = $430 left in her bank account.

2). $430 + $200 = $630 in her bank account.

3). $630 - $89 = $541 left in her bank account.

(Withdraw means removing some of your money out of your bank account, and deposit means putting money back in your bank account)

So, therefore, after all of those transactions, Ms. Lawrence's bank account has $541.

Hope this helps! <3

9514 1404 393

Answer:

  see the attachment

Step-by-step explanation:

The cost when no sugar is transported is 3250, so that is the "y-intercept". (There is no "y". The vertical axis is labeled "c", so that  is the c-intercept.)

The cost per ton is 125, so that is the slope or "rate of change". Each increase of 1 unit in the value of "s" will result in an increase of 125 in the value of "c". The grid lines for "c" are 500 apart, so 1 vertical grid space will correspond to 500/125 = 4 horizontal grid spaces.

The graph starts at the left side halfway between 3000 and 3500. It goes up 1 grid square for each 4 grid squares to the right.

Answer:

40 cm

Step-by-step explanation:

You do your area divided by your width I think (don't trust my answer)

Answer:

2

Step-by-step explanation:

Find the diagram attached

The Base of the triangle will be equivalent to the the length of the rectangle

Since the base of the triangle is 5units, hence length of the rectangle is 5units

Similarly, the height of the triangle is corresponding to the width of the rectangle

Since the height of the triangle is 2 units, the rectangle will be 2 unts wide. Hence the required answer is 2units

123.7 cm = 1.237 meters

hope it helps.

Step-by-step explanation:

Plug in x where you see large candle and y for small candle

64= 3x + 4y

64+4= x+ 8y