draw a line for the axis of symmetry of function f. also mark the x-intercept(s), y-intercept, and vertex of the function.f(x) = -(x 1)2 4

On solving the question we can say that So the probability of winning is 1/30 or about 0.0333. 

Probability theory is the branch of mathematics that calculates the probability that an event or statement is true. Risk is a number between 0 and 1, with 1 indicating certainty and a probability of about 0 indicating the likelihood that the event will occur. Probability is the probability or mathematical expression of probability that a particular event will occur. Alternatively, the probability can be specified as an integer between 0 and 1 or as a % between 0% and 100%. The proportion of events in decisions that are equally likely to lead to a particular event compared to all other outcomes. 

To create a surface model, you need to create a grid with one axis representing the square bag tiles and the other axis representing the circular bag tiles. Then shade the cells that represent the yellow squares and red circles that will be selected.

The win rate is equal to the area of ​​the shaded cells divided by the total area of ​​the grid.

Here is the surface model diagram:

| | YS | BS | RS |

---|----|----|----|

YC | YS | | | | |

---|----|----|----|

BC | | | BS | | |

---|----|----|----|

RC | RC | | | RS |

Shaded cells represent events that select yellow squares and red circles. The only way to do this is to select the yellow square from the bag of squares and the red circle from the bag of circles. So the odds of winning are:

P(win) = area of ​​shaded cells / total area of ​​grid

= 1 / (5 * 6)

= 1/30

So the probability of winning is 1/30 or about 0.0333. 

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Answer:

$1,305

Step-by-step explanation:

14500x0.09=1,305

The probability that Rosa's mom chooses sausage and onion is: 1/8C₂.

Probability refers to the chance of an event occurring. It is given by the formula: number of favorable outcomes/number of total outcomes. The total number of groups from which Rosa's mom can make her choice is 1 and this is the number of favorable outcomes.

But, the total number of outcomes that Rosa can hope to expect are 2 two toppings(sausage or onions) out of 8. So, the selected answer is the representation of the probability.

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An example of inductive reasoning is hypothesizing that students in the back row will score lower on exams; the hypothesis was developed because the test scores of the students in the back row are generally low  is True.

An example of inductive reasoning is hypothesizing that students in the back row will score lower on exams based on the observation that the test scores of the students in the back row are generally low. Inductive reasoning involves making generalizations or forming hypotheses based on specific observations or patterns. In this case, the hypothesis is derived from specific instances (the test scores of students in the back row) and is used to make a general claim about students in the back row scoring lower on exams.

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Answer:

hope this helps!:)

The coordinates of S(-7,1) after a reflection over the line y = 3 is given as follows:

(-7,5).

The coordinates of the original point in this problem are given as follows:

S(-7,1).

The reflection line is given as follows:

y = 3.

The reflection line is an horizontal line, meaning that:

The y-coordinate of S is 2 units below of the reflection line, hence after the reflection it will be two units above, as follows:

3 + 2 = 5.

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Expressions 2(-3)(7), -2(27 ÷ 9), and (4 - 10) - (8 ÷ (-2)) all have negative values.

The expressions that have negative values are:

1. 2(-3)(7)
2. -2(27 ÷ 9)
3. (4 - 10) - (8 ÷ (-2))

Let's break down each expression to understand why they have negative values.

1. 2(-3)(7):

  - First, we multiply -3 and 7, which gives us -21.
  - Then, we multiply 2 and -21, which gives us -42.
  - Therefore, the expression 2(-3)(7) has a negative value of -42.

2. -2(27 ÷ 9):

  - We start by calculating 27 ÷ 9, which equals 3.
  - Then, we multiply -2 and 3, which gives us -6.
  - Hence, the expression -2(27 ÷ 9) has a negative value of -6.

3. (4 - 10) - (8 ÷ (-2)):

  - Inside the parentheses, we have 4 - 10, which equals -6.
  - Next, we have 8 ÷ (-2), which equals -4.
  - Finally, we subtract -4 from -6, which gives us -6 - (-4) = -6 + 4 = -2.
  - Thus, the expression (4 - 10) - (8 ÷ (-2)) has a negative value of -2.

To summarize, the expressions 2(-3)(7), -2(27 ÷ 9), and (4 - 10) - (8 ÷ (-2)) all have negative values.

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Answer:

F ' = (-2, 1)

G ' = (2, -2)

H ' = (4, 3)

========================================

Explanation:

The rule \((\text{x},\text{y})\to (\text{x},-\text{y})\) reflects any point over the x axis.

We keep the x coordinate the same. The y coordinate flips from positive to negative, or vice versa.

For example, let's use that rule on point F.

\((\text{x},\text{y})\to (\text{x},-\text{y})\\\\(-2,-1)\to (-2,-(-1))\\\\(-2,-1)\to (-2,1)\\\\\)

Therefore, point F ' is located at (-2,1).

Follow that same logic for points G and H.

Let me know if you need to see the steps for the other points.

Answer:

0 < x < 18

Step-by-step explanation:

The rule for triangles is that one side must be less than the sum of the other two sides.

x < 9+9

9+x > 9

Answer

The transformation is a dilation with a scale factor of 2.

Explanation

The vertices of the triangle are given as A (1, 3), B(4, 2), and C (3, 8).

Which transformation would produce an image with vertices

A' (2, 6), B'(8, 4), C'(6, 16)?

As we can see from the solution of the transformation, the new coordinates are double the given coordinates.

A rotation, 90º clockwise or anticlockwise interchanges the x and y coordinates somewhat.

A reflection does this interchanging too.

But a dilation with a scale factor changes the size of the figure by multiplying the coordinates of the vertices by the value of the scale factor.

Since the new coordinates are double of the old coordinates, we can see that this transformation is a dilation with a scale factor of 2.

Hope this Helps!!!

Answer: (x-6)(x+1)

Step-by-step explanation:

Sum :  x2 − 5  x- 6

x2 + x-=6 x − 6

factor pair: x  2 + x − 6 x − 6

x( x+ 1 ) − 6 ( x + 1 )

rewrite from: x (x  + 1 ) − 6 ( x + 1 )

(x-6)(x+1)

Answer:

A: (x-6)(x+1)

Step-by-step explanation:

We need to find 2 numbers that add to make -5 and multiply to make -6.

We already have the numbers infront of us, so by process of elimination we can remove B and D.

For the numbers, we need a positive number and a negative number (two negatives make a positive). We can eliminate C because at first -3 multiplied by 2 is -6. However, when -3 is added to 2 we get -1.

If we expand A, it makes the expression that needs to be factorised because...

-6 × 1 = -6

-6 + 1 = -5

So expanding it properly we get.

x² - 6x + x - 6

Simplify.

x² - 5x -6

The valid reasons to use a sample instead of evaluating a much larger population are contacting the whole population would be only marginally more accurate than a sample. A sample can be chosen to validate a specific idea about the population.

Contacting the entire population would be time consuming.
1. Contacting the whole population would be only marginally more accurate than a sample: This is a valid reason because a well-designed sample can often provide an accurate estimate of the population, while using significantly fewer resources.
2. Sampling is a random process, and therefore more accurate than measuring the whole population: This statement is incorrect. A random sample can provide an unbiased estimate, but it is not necessarily more accurate than measuring the entire population.
3. A sample can be chosen to validate a specific idea about the population: This is a valid reason because sampling can be used to test hypotheses or ideas about the population without having to evaluate every member of the population.
4. Contacting the entire population would be time-consuming: This is a valid reason because sampling can save time and resources compared to attempting to gather data from every individual in a population.

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Answer: 60

Step-by-step explanation:

The midpoint for any segment/line when you're given the start and end point of the line as A=(x1,y1) and B=(x2,y2) is

(   ((x1 + x2) /2), ((y1 + y2)/2)   )

So here the point is

(  (-2+6)/2), (-6+12)/2)  )

= (2, 3)

So it's the second option

The derivative dw/dz of the function w = 3z^3 - 723z + 2122 at z = 1 is -714.

To find the derivative dw/dz of the function w = 3z^3 - 723z + 2122 at z = 1:

Follow these steps:

STEP 1: Identify the function: w = 3z^3 - 723z + 2122
STEP 2: Differentiate the function with respect to z:
  dw/dz = d(3z^3)/dz - d(723z)/dz + d(2122)/dz
STEP 3: Apply the power rule for derivatives:
  dw/dz = 3(3z^2) - 723(1) + 0
STEP 4: Simplify the derivative:
  dw/dz = 9z^2 - 723
STEP 5: Evaluate the derivative at z = 1:
  dw/dz = 9(1)^2 - 723
  dw/dz = 9 - 723
  dw/dz = -714

So, the derivative dw/dz of the function w = 3z^3 - 723z + 2122 at z = 1 is -714.

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Answer:

x=2/3 or x=1

Step-by-step explanation:

Factor 3x² and 2

The length of the YZ for the two similar triangles will be 9 inches.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

Given that triangle, ABC is similar to triangle XYZ. The value of the side YZ will be calculated by the similarity property,

YZ / BC = XZ / AC

x / 3 = 15 / 5

x = ( 15 x 3 ) / 5

x = 3 x 3

x = 9 inch

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he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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Answer:

y - 1 = (3/5)x

Step-by-step explanation:

First find the slope of this line.  As we move from (0, -2) to (5, 1), x (the 'run') increases by 5 and y (the 'rise') increases by 3.  Thus, the slope of this line is m = rise / run = 3/5.

Using the point-slope formula for the equation of a straight line:

y - 1 = (3/5)(x - 5), or

y - 1 = (3/5)x                This can also be written as 5y - 5 = 3x, or

y = (3/5)x + 1

Answer:

y=3−x

(−2,0,3)

The probability of getting exactly one face card is 0.72.

According to the questions two cards are drawn from a deck.

Since, we know that

Total number of cards in a deck = 52

Total number of face cards =  3 × 4 = 12

So, the number of ways of selecting 2 cards from a deck = \(^{52} C_{2}\)

And, the total number of ways of  getting exactly one face cards

= \(^{12} C_{1} \times ^{40} C_{1}\)  + \(^{40} C_{1} \times ^{12} C_{1}\)

= 2\(^{40} C_{1} \times ^{12} C_{1}\)

Therefore, the probability of getting exactly one face card

= \(\frac{2(^{40} C_{1} \times ^{12} C_{1})}{^{52C_{2} } }\)

\(= \frac{2(\frac{40 \times 39!}{1!\times 39!} \frac{12\times 11!}{11!}) }{\frac{52\times 51\times 50!}{2!\times50!} }\)

\(= \frac{2(40\times 12)}{26\times 51}\)

\(=\frac{2\times 480}{1326}\)

= 0.72

Hence, the probability of getting exactly one face card is 0.72.

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Answer:

Step-by-step explanation:

dava kaAjbhm

1) In this question, we can notice that theta is in Quadrant IV. In this quadrant, the cosine of theta yields a positive value.

2) So, let's make use of a Pythagorean Identity to find the value of the cosine of theta, given the sine of that same angle:

3) Thus the cosine of theta is 4/5 for in Quadrant IV cosine is positive.

Using Laws of exponents, the solution is: 7³

There are different laws of exponents such as:

- When multiplying by similar bases, keep the same base and add exponents.

- When you raise the base to the first power to another power, keep the same base and multiply by the exponent.

- For equal base division, subtract the denominator exponent from the numerator exponent, keeping the bases the same.

We are given the expression:

(15 - 8)¹¹/[(6 + 1)²]⁴

Simplifying the numerator gives:

7¹¹

Simplifying the denominator gives: 7⁸

Thus, we now have:

7¹¹/7⁸

Applying laws of exponents gives:

7¹¹⁻⁸ = 7³

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Proof by contradiction is a type of indirect reasoning that involves assuming the opposite of the statement to be proved and then deriving a contradiction. It is a common method in mathematical proofs.

A proof by contradiction is a method of indirect reasoning that is often used in mathematics to prove a statement. The method involves assuming the opposite of the statement to be proved, and then deriving a contradiction. This contradiction shows that the assumption was incorrect, and therefore the original statement must be true.

For example, suppose we want to prove that the square root of 2 is an irrational number. We assume the opposite, that the square root of 2 is a rational number. This means that there exist two integers p and q such that the square root of 2 equals p/q.

We can then manipulate this equation to show that p and q have a common factor, which contradicts the assumption that p and q are integers with no common factors. Therefore, we can conclude that the square root of 2 is indeed an irrational number.

Proof by contradiction is a powerful method of reasoning that allows us to prove many mathematical statements. However, it can sometimes be difficult to apply, and alternative methods may be used in some cases.

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The value of x which is the length of the base of the triangle in the question is; 29 meters

A triangle is a three sided polygon, with three interior angles.

Please find attached the possible diagram in the figure, (created with MS Word), which is a question from a mathematics textbook posted on the internet

The diagram indicates that the altitude or height of the triangle = 8 meters

The specified area of the triangle is; A = 261 square meters

The base length of the triangle = x

The formula for the area of a triangle, A, is; A = (1/2) ×Base length × Height

Therefore;

A = 261 m² = (1/2) × x × 18 m

x = 261 m² ÷ ((1/2) × 18 m) = 29 m

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