rewrite y(x)=2(x-3)^2-9 standard form

The probability that both bills are $100 bills when selecting two bills at random with replacement from the hat is 1/16.

To find the probability that both bills are $100 bills when selecting two bills at random with replacement from a hat containing a $5, $10, $20, and $100 bill, we'll first construct a sample space and then calculate the probability.
Step 1: Construct the sample space.
Since there are four bills and we're selecting two with replacement, there are a total of 4 x 4 = 16 possible outcomes. The sample space is as follows:
{$5, $5}, {$5, $10}, {$5, $20}, {$5, $100},
{$10, $5}, {$10, $10}, {$10, $20}, {$10, $100},
{$20, $5}, {$20, $10}, {$20, $20}, {$20, $100},
{$100, $5}, {$100, $10}, {$100, $20}, {$100, $100}.

Step 2: Determine the probability that both bills are $100 bills.
In the sample space, there's only 1 outcome where both bills are $100 bills: {$100, $100}. Since there are 16 possible outcomes in total, the probability of both bills being $100 bills is:
1 (desired outcome) / 16 (total outcomes) = 1/16

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Answer:

x= 50!

Step-by-step explanation:

To find the hypotenuse, add the squares of the other sides, then take the square root.

Craig's superannuation will be worth of $22,099.77 at the end of 15 years.

Given that Craig made 4 investments of $500 in four years. To find out the superannuation we have to find the remaining 11 investments he made in the remaining 11 years from a total of 15 years.

For the first four investments,

a = $500

r = 1.087  [ given interest rate is 8.7% per annum ]

n = 4

By, substituting all these values in the given equation,

S1 = [tex]\frac{500(1-1.087^{4}) }{1-1.087}[/tex]  = $6194.64

Similarly for the remaining 11 years,

a = $900

r = 1.087

n = 11

S2 =  [tex]\frac{500(1-1.087^{11}) }{1-1.087}[/tex] = $16,905.13

Total superannuation = S1 + S2 = $6194.64 + $16,905.13 = $22,099.77.

From the above explanation, we can conclude that Craig's total superannuation will be worth $22,099.77

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To provide an accurate answer, I would need more context about the data and the research question being asked. However, I can provide a brief explanation of each test option:

a. Single sample t-test: Used when comparing a sample mean to a known population mean.
b. Independent t-test: Used when comparing the means of two independent groups.
c. Paired t-test: Used when comparing the means of two related groups or repeated measures.
d. One-way ANOVA: Used when comparing the means of three or more independent groups.

Please provide more information about the data and research question so I can recommend the appropriate test to analyze the data.

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The cost of the souvenir is approximately $15.92.

Let's assume the cost of the souvenir is S.

According to the given information, the cost of the burger is 1/4 of the cost of the souvenir, which means the cost of the burger is (1/4)S.

The cost of the pass is 2/3 of the cost of the souvenir, which means the cost of the pass is (2/3)S.

Hannah had $2.00 left over after buying these items, so we can write the equation:

$40.50 - (1/4)S - S - (2/3)S = $2.00

To solve for S, we'll combine like terms:

$40.50 - (9/12)S - (12/12)S - (8/12)S = $2.00

$40.50 - (29/12)S = $2.00

Next, we'll isolate the variable by subtracting $40.50 from both sides:

-(29/12)S = $2.00 - $40.50

-(29/12)S = -$38.50

To solve for S, we'll divide both sides by -(29/12):

S = (-$38.50) / -(29/12)

S ≈ $15.92

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The correct equation can be given by;  2,500 = 125(2)^w. Option D

If we have a sentence that we want to convert to equation;

We can see that the beekeeper finds that the initial population of 125 bees doubles each week thus the correct equation is; 2,500 = 125(2)^w.

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The correct equation can be given by;  2,500 = 125(2)^w. Option D

How do you form equation from sentence?

If we have a sentence that we want to convert to equation;

Determine the mathematical relationships or procedures that are being described by carefully reading the statement.

Any unknown quantities in the phrase should be given variables.

To represent the processes or relationships, use conventional mathematical symbols.

Create a clear and succinct written version of the equation.

We can see that the beekeeper finds that the initial population of 125 bees doubles each week thus the correct equation is; 2,500 = 125(2)^w.

Answer: To find the number of meters in 20,000 leagues, we first need to convert the number of leagues to miles:

20,000 leagues * 3.452 miles/league = 69,040 miles

Next, we can convert the miles to meters:

69,040 miles * 1609.3 meters/mile = 111,030,472 meters

So the number of meters in 20,000 leagues is approximately 111,030,472 meters. To round this to the nearest whole number and use it as the value of x in the title, we can round it to:

x = 111,030,472 rounded to the nearest whole number = 111,030,000 meters

Therefore, Jules can call his most recent work "111,030,000 meters under the sea".

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=2\\ h=1.6\\ A=2.2 \end{cases}\implies 2.2=\cfrac{1.6(2+b)}{2} \\\\\\ 4.4=1.6(2+b)\implies \cfrac{4.4}{1.6}=2+b\implies 2.75=2+b\implies \boxed{0.75=b}[/tex]

The predicted value of the car after 5 years is $6,000 (rounded to the nearest dollar).

To predict the car's value after 5 years, we can use a linear regression model. We will use the data points given in the problem statement to find the equation of a straight line that fits the trend in the data. Once we have this equation, we can plug in the value of 5 for x to predict the corresponding value of y, which represents the car's value after 5 years.

Using the data points (1, 18000) and (3, 12000), we can find the slope of the line:

slope = (y2 - y1) / (x2 - x1) = (12000 - 18000) / (3 - 1) = -3000

Next, we can use the slope-intercept form of a line to find the equation of the line:

y = mx + b, where m is the slope and b is the y-intercept

Using the point (1, 18000) and the slope we just found, we can solve for b:

18000 = -3000(1) + b

b = 21000

So, the equation of the line is:

y = -3000x + 21000

To predict the car's value after 5 years, we can plug in x = 5 and solve for y:

y = -3000(5) + 21000 = 6000

Therefore, the predicted value of the car after 5 years is $6,000 (rounded to the nearest dollar).

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Answer: if a column contains a leading 1 then the rest of the entries in that column are zeroes

Step-by-step explanation:

The equation represents how many more containers they can use on their float will be 153x + 19,125 = 367,200. Then the correct option is A.

Already, 19,125 flowers have been fastened to the Happy Campers' float. Say they utilize additional x pots with 153 blooms each. In that case, there would be the following number of flowers on their float:

19,125 + (x × 153)

The calculation that illustrates how many more containers they may utilize since they are only allowed to put 367,200 flowers on their float is:

19,125 + (x × 153) ≤ 367,200

153x + 19,125 ≤ 367,200

Thus, the correct option is A.

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The Height ≈ 4 cm and the Slant height ≈ 5 cm.

To solve for the height and slant height of the cone, we first use the formula for the surface area of a cone:

where r is the radius of the base, ℓ is the slant height, and π is approximately 3.14.

Since we are given the surface area (75.4 cm²) and the radius (3 cm), we can substitute these values into the formula and solve for ℓ:

Now that we have the slant height, we can use the Pythagorean theorem to find the height, h:

Rounding to the nearest whole number, we get the height ≈ 4 cm and the slant height ≈ 5 cm.

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The algebraic expression for 3 added to X as required in the task content is; x + 3.

The algebraic expression for 2 subtracted from x as required in the task content is; x - 2.

It follows from the task content that the algebraic expression which represents the given word phrases are to be determined.

There, for the word phrase 3 added to x; we have; x + 3.

On the other hand, for the word phrase; 2 subtracted from x; we have; x - 2.

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Factoring quadratics is a technique used to simplify and solve quadratic equations. When the leading coefficient (a) of the quadratic equation is not equal to 1, it becomes slightly more complicated to factor. To factor quadratics when a does not equal 1, one must use a method called grouping.

The first step is to multiply the coefficient of the leading term (a) by the constant term (c) of the quadratic equation. This gives you two numbers that add up to the coefficient of the middle term (b). These two numbers will be used to group the terms in the quadratic equation.

Next, the quadratic equation is split into two parts, where each part includes two terms that are grouped based on the two numbers obtained in the first step. From here, factoring can be done using the distributive property.

Once the equation is factored, it can be solved by setting each factor equal to zero and solving for the variables. It's important to remember to check solutions by plugging them back into the original equation.

In conclusion, factoring quadratics when a does not equal 1 involves using a method called grouping to factor the equation. This technique is slightly more complicated than when a equals 1, but it can still be easily mastered with practice.

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Answer:

a = 14.3

Step-by-step explanation:

Since you have a right triangle you can use the Pythagorean Theorem.

a^2 + b^2 = c^2

we know b and c, so fill them in.

b = 14, c = 20 (this was given in the question)

a^2 + 14^2 = 20^2

simplify the squares.

a^2 + 196 = 400

subtract 196

a^2 = 204

square root both sides.

a = sqrt204

(use a calculator for this part)

a = 14.2828568571

round to the nearest tenth (one decimal place)

a = 14.3

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's assume that side m and side n are the two legs of the right triangle, and side p is the hypotenuse. According to the Pythagorean Theorem, the relationship between these sides can be written as:

m^2 + n^2 = p^2

To find the measure of side m, we would need more information about the lengths of sides n and p. However, this equation shows the relationship between the three sides of the triangle and can be used to determine the length of side m when given the lengths of sides n and p.

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The Columbia Power Company experiences power failures with a mean of µ=210 per day. To find the probability that there are exactly two power failures in a particular day, we can use the Poisson probability formula:

P(x) = (e^(-µ) * (µ^x)) / x!

In this case, x = 2 (since we want to find the probability of exactly two power failures) and µ = 210. Plugging in the values, we get:

P(2) = (e^(-210) * (210^2)) / 2!

Calculating this expression, we get P(2) ≈ 0.018. So, the probability that there are exactly two power failures in a particular day is approximately 0.018.

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Answer:

to get y easily you have to substitute for x in the first equation. the answer is A

Step-by-step explanation:

proving it:

-3=5y-2(-4)

-3=5y+8

then you can collect the like terms to get the final answer.

0.3737373737... is a rational number and can be written as the ratio of two integers 37 and 99.

Let x = 0.3737373737...

Multiplying both sides of the equation by 100, we get:

100x = 37.37373737...

Subtracting x from 100x, we get:

99x = 37

Hence, x = 37/99, which is a rational number.

Therefore, we have shown that 0.3737373737... is a rational number and can be written as the ratio of two integers 37 and 99.

To check our answer, we can simplify 37/99 by dividing both the numerator and denominator by their greatest common factor, which is 1. This gives us the same expression, 37/99, confirming that it is indeed a rational number.

In general, any decimal that has a repeating pattern can be written as a ratio of two integers and is therefore a rational number. This is because the repeating pattern can be expressed as a finite sequence of digits that can be represented as a fraction with a power of 10 in the denominator, which can be simplified to a ratio of two integers.

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The minimum intercept of line CD on the y-axis is 1.

Since AB is on the line y=2x-17, we can write the equation of the line as y=2x-17. We know that AB is a side of a square, so its length is equal to the distance between A and B. Therefore, we need to find the coordinates of A and B. Since the square is symmetric with respect to the line y=2x-17, the x-coordinate of the midpoint of AB is (17/2). Therefore, the x-coordinates of A and B are (17/2)-s and (17/2)+s, where s is half the length of AB.

Now, we need to find the value of s. Since AB is a side of a square, it is equal in length to the distance between C and D. We can find the equation of the line CD by using the coordinates of C and D, which are (x, x²) and (y, y²), respectively. Substituting these coordinates into the equation of the line, we get:

Solving for x and y in equations 1 and 2, we get:

Since AB is a side of a square, its length is equal to the distance between C and D, which is:

√[(y^2-x²)²+(y-x)²]

= √[(2√18)²+2²]

= 2√82

Therefore, s = √82.

Finally, we can find the y-intercept of CD by plugging in x=0 into the equation of the line CD, which is:

Substituting the values of x and y, we get:

Therefore, the minimum intercept of line CD on the y-axis is 1.

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The complete question is:

Consider one sides AB of a square ABCD in order on line y=2x−17, and other two vertices C, D on y=x². The minimum intercept of line CD on the y-axis is

Answer: There are 7 quarts for 28 cups.

Step-by-step explanation:

1 quart equals 4 cups.

28/4=7

Answer: 7

Step-by-step explanation:

-29/5 is rational and can be expressed as a ratio of two integers (-29 and 5).

To show that -29/5 is rational, we need to express it as a ratio of two integers.

We know that -29 is an integer and 5 is also an integer. Therefore, we can write:

-29/5 = (-29) / 5

Since both -29 and 5 are integers, their ratio is a rational number. Therefore, -29/5 is also a rational number.

Another way to see this is to note that any fraction a/b can be written in lowest terms as:

a/b = p/q

where p and q are integers with no common factors (other than 1). To find p and q, we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF). In this case, the GCF of -29 and 5 is 1, so -29/5 is already in its simplest form.

Therefore, -29/5 is rational and can be expressed as a ratio of two integers (-29 and 5).

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Decision analysis is the study of the possible payoffs and probabilities associated with a decision alternative or a decision strategy in the face of uncertainty.

This approach helps decision-makers evaluate various options and make informed choices under uncertain conditions.

The study of the possible payoffs and probabilities associated with a decision alternative or a decision strategy in the face of uncertainty is known as decision analysis.

Decision analysis is a systematic approach to decision-making that uses mathematical and statistical tools to evaluate different alternatives and their associated risks and rewards.

It involves identifying the possible alternatives, the possible outcomes, and the likelihood of each outcome, and then using this information to select the best course of action.

Decision analysis is commonly used in a wide range of fields, including business, engineering, healthcare, and environmental management.

In business, decision analysis is often used to evaluate investment opportunities, new product development, and strategic planning.

In engineering, decision analysis is used to evaluate design options and project risks.

In healthcare, decision analysis is used to evaluate treatment options and medical technology.

In environmental management, decision analysis is used to evaluate the risks and benefits of different policies and regulations.

The key steps in decision analysis include defining the problem, identifying alternatives, assessing probabilities, evaluating outcomes, and selecting the best alternative.

This involves a range of techniques, such as decision trees, utility theory, sensitivity analysis, and Monte Carlo simulation.

These techniques help decision-makers to evaluate the trade-offs between risks and rewards and make informed decisions in the face of uncertainty.

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You would need to put approximately $19,500 into the CD now in order to have $10,920 in 8 years.

To determine how much you must put into the CD now, we can use the formula for simple interest:

I = P * r * t

Where:

I is the interest earned

P is the principal amount (initial investment)

r is the interest rate

t is the time in years

In this case, we know the interest rate is 7% (or 0.07) and the time is 8 years. We want to find the principal amount (P) that will result in $10,920 in 8 years. So we rearrange the formula to solve for P:

P = I / (r * t)

Substituting the given values:

P = 10,920 / (0.07 * 8)

P = 10,920 / 0.56

P ≈ $19,500

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1. The total number of goals for the 15 matches is 43.

2. To show that Σ u² = 58, we use Σ(u - 1)² = 25

Σ(u - 1)² = 25 ⇒ Σ(u² - 2u + 1) = 25

Σu² - 2Σu + Σ = 25 ⇒ Σu² - 2(24) + 15 = 25

Σu² = 25 + 48 - 15 → Σu² = 58

3. The variance of the teams together is 39.311

1. To find the total number of goals, we must establish that Σ(u + x) is the total number of goals.

TNG = Σu + Σx

Given that Σ(u - 1) = 9, it becomes
Σu - 15 = 9 ⇒ Σu = 9 + 15

Σu = 24

Given that Σu = 24 and Σx = 19

TNG = 24 + 19 = 43

we say

43 ÷ 15 = 2.866
We already know that Σx² = 39, Σu² = 58.

Σ(u - 1)Σx = 9 × 19 = 171

Σux - Σx = 171

Σux - 19 = 171

Σux = 190

Σt² = 58 + 2(190) + 39

= 58 + 380 + 39

= 477

Variance = 477

                 15 - 2.866

Variance = 477/12.134

Variance = 39.311

The answer provided is based on the full question below;

Each year Upchester United plays against Upchester City in a local derby match. The number of goals scored in a match by United is denoted by u and the number of goals scored in a match by City is denoted by c.

The number of goals scored in the past 15 matches are summarized by

Σ(u - 1)² = 25,  Σ(u - 1) = 9  Σx² = 39 and  Σx = 19

a How many goals have been scored altogether in these 15 matches?

b Show that Σu² = 58.

c. Find, correct to 3 decimal places, the variance of the number of goals scored by the two teams together in these 15 matches.​

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The correct answer is (d) all of the above.

The standard normal distribution is a special case of the normal distribution, where the mean is equal to 0 and the standard deviation is equal to 1. It is also sometimes called the "z-distribution" or "z-score distribution," because it is often used to calculate z-scores, which measure the distance between an observation and the mean in units of the standard deviation. Therefore, all of the statements (a), (b), and (c) are true.

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The value of x is 1.5 and value of y is 1.8 from the given triangle.

In the right triangle let us find the hypotenuse

9²+6²=x²

81+36=x²

117=x²

Take square root on both sides

√117=x

x=10.8=11

11/y=6

value y=11/6=1.8

9/x=6

x=9/6

=1.5

Hence, the value of x is 1.5 and value of y is 1.8 from the given triangle.

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