Look at this diagram:

A possible definition for function f(x) is given as follows:

y = -2x² - 2.

According to the Factor Theorem, the function f(x) can be defined according to it's zeros, as follows:

f(x) = a(x - x')(x - x'').

In which:

Two of the points of the function are (1,0) and (-1,0), hence the zeros are given as follows:

x' = 1, x'' = -1.

Then the function can be defined as follows:

f(x) = a(x - 1)(x + 1)

f(x) = a(x² - 1).

When x = 0, y = 2, hence the leading coefficient a is obtained as follows:

2 = a(0 - 1)

-a = 2

a = -2.

Thus the complete definition of the function is of:

y = -2(x² - 1)

y = -2x² - 2.

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The statement which is true for the inequality will be equal to 9 > -5, so 9 is located to the right of -5 on a horizontal number line.

A straight line of numbers is shown visually as a number line. This line is employed to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals.

As per the given inequalities given in the question,

1.

-10 > -15, so -10 is located to the left of -15 on a horizontal number line.

The statement is wrong because -10 is located on the right side of -15

2.

8 > -13, so 8 is located to the left of -13 on a horizontal number line.

The statement is wrong because 8 is located on the right side of -13.

3.

9 > -5, so 9 is located to the right of -5 on a horizontal number line.

This statement is true, that 9 is located to the right of -5.

4.

-6 < 1, so -6 is located below 1 on a vertical number line.

This statement is true, that -6 is located to the below of -5.

5.

-14 > 7, so -14 is located below 7 on a vertical number line.

This statement is false.

6.

11 < -13, so 11 is located to the right of -13 on a horizontal number line.

This statement is also false.

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The example of rational function is option(1) which is f(x)=3x²+1 over x-1

What is Rational Function ?

Hence, the example of rational function is option(1) which is f(x)=3x²+1 over x-1.

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Answer:

(1,-6)

Step-by-step explanation:

Ordered pairs are (x,y)

The vertex of the quadratic formula is its lowest point if opening up, and its highest point if opening down

This one opens up so it is the lowest point

The x value of the vertex is x=1

the Y value of the vertex is y=-6

Answer: 3 47/126

Step-by-step explanation: You have to find the common denominator to make the problem easy and make sense. I highly recommend using a fraction calculator if you aren't sure how to do it.

Jon still needs to travel miles to Sacramento, according to a linear equation: Y=-55x +600 .

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

The meanings of the word equation and its cognates in various languages can vary slightly.

For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.

Finding the values of the variables that result in the equality is the first step in solving an equation with variables.

The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions.

Equations come in two varieties: identities and conditional equations.

Hence, Jon still needs to travel miles to Sacramento, according to a linear equation: Y=-55x +600 .

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Answer:

Step-by-step explanation:

The product of the given numbers is, [tex]-7\frac{7}{16}[/tex].

What is product?

One of the four fundamental arithmetic operations, along with addition, subtraction, and division, is multiplication. A product is the output of a multiplication operation.

The outcome of multiplying two or more numbers together in mathematics is called the product. With the help of examples, learn more about the product of fractions and decimals.

Given:

2 and one-eighth times negative 7 times five tenths.

We have to determine the product.

[tex]2\frac{1}{8} (-7)(\frac{5}{10} )[/tex]

Convert improper fraction into a fraction

[tex]2\frac{1}{8} = \frac{(2)(8)+1}{8} = \frac{17}{8}[/tex]

⇒

[tex](\frac{17}{8} )(-7)(\frac{1}{2}) \\-\frac{119}{16} \\-7\frac{7}{16}[/tex]

Hence, the product of the given numbers is, [tex]-7\frac{7}{16}[/tex].

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Answer:

20090089$

Step-by-step explanation:

Answer: $359

Step-by-step explanation:

I got the same problem on DeltaMath- You use the formula A = P ( 1 + r/n ) ^nt

P = 4700

R = 0.055

T = 12

N = 4

You plug it in to get 9052.7283 and then subtract 8693.386 to get 359.3423 which rounds to 359

The anticipated total number of heads produced by this method is 1/2n=N when fair coin is tossed n times, and the results are tallied by counting the heads.

Given that,

A fair coin is tossed n times, and the results are tallied by counting the heads. The coin is then thrown a further n times.

We have to calculate the anticipated total number of heads produced by this method.

We know that,

Either head or tail will appear when a coin is tossed.

The sample space of a random experiment is the collection of all feasible results. Therefore, if your random experiment involves flipping a coin, the sample space is "Head, Tail," or more tersely, "H, T."

So,

1/2n=N

Therefore, the anticipated total number of heads produced by this method is 1/2n=N when fair coin is tossed n times, and the results are tallied by counting the heads.

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The equation used to represent the situation:

Cost per pound = Total Cost of Turkey / Number of Pounds

A formula known as an equation uses the equals sign to express how two expressions are equal. The meanings of the word equation and its translations into other languages might vary slightly; Finding the values of the variables that cause the equality to be true is the first step in solving an equation with variables.

Quantity = 19 pounds

Total Cost = $25.65

Now to calculate the cost of Turkey per pound, we can use the following equation:

Cost of Turkey per pound = Total Cost / Quantity of Pounds

Cost per pound = 25.65 / 19

Therefore, the cost of turkey per pound = $1.35

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-480 ÷ 8 = -60

2x = -120

-20 × 3 = -60

(2 × 3) × (-5 × 2) = -60

C. The slope of the graph is 1/3

Slope = (y2 - y1) ÷ ( x2- x1)

y2= 5, y1=2, x2=9, x1=0

y2-y1 = 5-2 = 3

x2-x1 = 9-0 = 9

Slope = 3/9 = 1/3

The orientation factor in a chemical reaction relates the frequency factor to the collision factor and depends on the extent of complexity of the reactants in a reaction.

Does the orientation factor depend on temperature?

The direction of the collision between the chlorine atoms and the ozone determines the pace of reaction; if the direction is incorrect, no reaction takes place. The right orientation will allow for response. The direction of collisions is independent of temperature.

According to the Collision Theory, molecules must collide with sufficient activation energy to break and re-form existing bonds, as well as with favorable spatial orientation, in order for a chemical reaction to occur.

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The percentage of 12-month-old baby boys who weigh is 0.5.

What is mean and standard deviation?

Mean=22.5; Standard deviation=2.2

The z-score for the given weight is

z−score ​= Blood pressure reading−Mean / Standard deviation

​= 23.6−22.5/2.2

= 1.1/2.2

​=0.5

Hence, the percentage of 12-month-old baby boys who weigh is 0.5

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Answer:

option c

Step-by-step explanation:

c. 9 billion people

Answer:

B. 9 Billion people

Step-by-step explanation:

The point (25,125) means that the monthly home heating bill was $5 for an average monthly temperature of 1°F.

From the question, we have the following parameters that can be used in our computation:

Point (25, 125)

This point can be expressed as

(x, y) = (25, 125)

The average monthly temperature bill is then calculated using the following equation

Average monthly temperature bill = y/x

Substitute the known values in the above equation, so, we have the following representation

Average monthly temperature bill = 125/25

Evaluate

Average monthly temperature bill = 5

Hence, the average monthly temperature = 5

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The students that still need to complete their assignments = 14

According to the given question,

The total number of students in Mr. Torres's class = 24

Now as the question tells us,

Mr. Torres instructed the students to read only if they have finished their assignments.

The percentage of the class that is reading = is 40% which means that 40% of the class has completed their assignments.

Now we have to calculate the number of students that are still doing their assignments,

⇒ 40 % of the 24

⇒ [tex]\frac{40}{100}[/tex] x 24

⇒ 0.4 x 24

⇒ 9.6 ≈ 10

So the students that have completed their assignments = 10

Students that are still doing their assignments,

⇒ 24 - 10

⇒ 14

Therefore, The students that still need to complete their assignments = 14

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Mr. Torres tells his class of 24 that when they have completed their assignment they may read at the end of class 40% of the class is reading how many students still need to complete their assignment

Let x is average for rest of seven test. Then average for remaining test is x= 2.27

The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

The middle point of the set of values is the mean. It represents the mean of the data set's values. In statistics, the centre number, also known as the mean, is referred to as the average.

We want the TOTAL average to equal 94

4/9 of the 5 scores have an average of 178

Let x = average of the 5 remaining test, which is worth 5/9 of the total average.

We get: 94 = (4/9)(178) + (5/59)(x)

94=712/9+59x/9

846=712+59x

846-712=59x

134=59x

134/59=x

Solve: x = 2.27

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In 1970, 92% of American 30-year-olds earned more than their parents did at age 30 (adjusted for inflation). In 2014, only 51% of American 30-is The probability is. 83

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

How is probability determined?

picture for "probability"

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood that something will occur by the likelihood that it won't.

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A triangle has three angles that measure 16˚, 38˚ and 126˚ will lead to

There are an infinite number of triangles produced when no side is specified.

The three angles produce an unlimited number of distinct triangles if side lengths are not provided.

The option that offered just angles—namely, angles of 16˚, 38˚ and 126˚—and no sides—meets the requirement for the production of an infinite number of triangle sides.

When there are options have sides or a side is provided, but not in accordance with that, to form an infinite number of triangles.

This condition forms infinite number of triangles

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Answer:

C) Infinite (More than one)

Step-by-step explanation:

The large figurine old for $12 each, and the mall figurine old for $8 each. The amount of money he received from the ale of the large figurine wa equal to the 42

Let x represent the number of large figurines that Kami sold.

Let y represent the number of small figurines that Kami sold.

This month kami sold 70 figurines in 2 sizes. This means that

x + y = 70 - - - - - - - - - - 1

The large figurines sold for $12 each and the small figurines sold for $8 each. The amount of money he received from the sales of the large figurines was equal to the amount of money he received from the sales of the small figurines. This means that

12x = 8y

y = 12x/8

y = 1.5x

Substituting y = 1.5x into equation 1, it becomes

x + 1.5x = 70

2.5x = 70

x = 70/2.5 = 28

y = 1.5x = 1.5 × 28 = 42

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The average acceleration of a bus that reaches a top speed of 14.2 m/s from rest in 22.8 seconds is 0.62 m/s².

Acceleration is the amount by which the velocity of something changes over a set period of time.

The formula to find the acceleration is a=(v-v₀)/t, where a=average acceleration, v=final velocity, v₀=initial velocity and t=time.

Given that, final velocity =14.2 m/s, initial velocity=0 and t=22.8 seconds.​

Now, the average acceleration is

a=(14.2-0)/22.8

= 14.2/22.8

= 0.62 m/s²

Therefore, the average acceleration of a bus that reaches a top speed of 14.2 m/s from rest in 22.8 seconds is 0.62 m/s².

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The unit rate of the graph that represents the proportional relationship is $12.5, which is below $13 per week. Therefore, Louis made the correct statement.

The graph of a proportional relationship is typically a straight line that runs through the point of origin (0, 0).

The slope of the graph gives the unit rate, which is calculated as m = y/x.

Given the graph that shows the proportional relationship between the number of weeks and the amount spent on coffee, we can use one point on the line, (4, 50) to find the unit rate, which will given us how much is spent per week.

Therefore:

Slope/unit rate or amount spent per week = y/x = 50/4 = $12.5.

Based on this, we can state that Louis is correct by saying Janie has not met her goal, because $12.5 per week is below the target of $13 each week.

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The probability that a bridge hand will have exactly 2 queens is 0.45%.

To find the probability of getting a bridge hand with exactly 2 queens, we need to use the binomial probability formula. The formula is:

P(exactly k successes) = (n choose k) * p^k * (1-p)^(n-k)

Where:

n is the total number of trials

k is the number of successes in the trials

p is the probability of success in a single trial

In this case, the total number of trials is 13 (since a bridge hand consists of 13 cards), and the number of successes we want is 2 (since we want exactly 2 queens). The probability of success in a single trial is the probability of drawing a queen, which is 4/52 (since there are 4 queens in a deck of 52 cards).

Plugging these values into the formula, we get:

P(exactly 2 queens) = (13 choose 2) * (4/52)² * (48/52)¹¹

= (78) * (1/169) * (4/13)¹¹

= (4/169) * (4/13)¹¹

This simplifies to:

P(exactly 2 queens) = (4/169) * (4/13)¹¹

= (4/169) * (4/169)¹¹

= (4/169)¹²

The final probability is approximately 0.0045 or 0.45%. This means that the probability of getting a bridge hand with exactly 2 queens is quite low.

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The coefficient x⁵ in expansion of (2x - 1)⁶ is; -192

We are given the expression;

(2x - 1)⁶

Using Pascals triangle, the coefficient of the terms here are;

1      6     15     20     15     6     1

The general formula for binomial expansion is;

(x + y)ⁿ = ⁿC₀xⁿy⁰ + ⁿC₁xⁿ⁻¹y¹ + ⁿC₂xⁿ⁻²y²+......+ ⁿCₙx⁰yⁿ

Thus, we can find the expansion of (2x - 1)⁶ as;

1[(2x)⁶ * (-1)⁰] + 6[(2x)⁵ * (-1)¹] + 15[(2x)⁴ * (-1)²] + 20[(2x)³ * (-1)³] + [15(2x)² * (-1)⁴] + [6(2x)¹ * (-1)⁵] + [1(2x)⁰ * (-1)⁶]

= 64x⁶ - 192x⁵ + 240x⁴ - 160x³ + 60x² - 12x + 1

The coefficient we are looking for is -192

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Answer:

Step-by-step explanation:

The best bank depends on the amount that Gerard will deposit. He can open an account with My bank and receive $100, or he can open with New bank and deposit lets say $5000 and he would receive an additional $250 because of the 5% bonus. It depends on the amount that Gerard is putting into the bank account when he opens it.

in the athletics team, tall members tend to win three times as many medals as short members.20 number of medals have been won by short athletes.

This question can be solved by using the ratio method. Since tall athletes are said to win three times as many medals as short athletes, this means that the ratio of tall athletes' medals to short athletes' medals is 3:1. We can use this ratio to calculate how many medals have been won by short athletes. Since the team has won a total of 60 medals, we can divide this number by 4 (the total number of medals in the ratio) to get 15. We then multiply 15 by the ratio of short athletes' medals (1) to get 15 medals. This means that short athletes have won 20 medals, since 15 multiplied by 3 is 45, leaving 60-45=15 medals for the short athletes. Thus, 20 medals have been won by short athletes.

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A 95% confidence interval with a 4% margin of error suggests that your statistic will be 95% of the time within 4 percentage points of the true population value.

A survey, may reveal that the 98% confidence interval is between 4.88 and 5.26. So, if the poll is repeated using the same methods, the true population parameter (parameter vs. statistic) will fall 98% of the time within the interval estimates (i.e. between 4.88 and 5.26).

The formal definition, on the other hand, includes a little more information. The margin of error in a confidence interval is defined as the range of values below and above the sample statistic. The confidence interval is a tool for demonstrating the level of uncertainty associated with a certain statistic (i.e. from a poll or survey).

In 2012, a Gallup poll (incorrectly) predicted that Romney would win the election, with Romney polling at 49% and Obama polling at 48%. The declared level of confidence was 95%, with a margin of error of 2. We can conclude that the results were computed to be 95% accurate within 2 percentage points.

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a^45d^9

To find the fifteenth term of the binomial expansion of (a³+d)24, we can use the binomial theorem, which states that the expansion of (a+b)n is given by the sum of the terms in the following formula:

(a+b)^n = a^n + na^(n-1)b + (n(n-1))/2a^(n-2)*b^2 + ... + b^n

Answer: 1,961,256a³⁰d¹⁴

Step-by-step explanation:

[tex]\displaystyle\\(x+y)^n \ is\ the\ binomial\ expansion \\\\The\ k\ term =C_n^{k-1}x^{n-k+1}y^{k-1}\\\\ n - the\ power \ of\ the \ binomial\\\\k - number\ of\ the\ term \ of\ the\ binomial[/tex]

                                        [tex](a^3+d)^{24}[/tex]

[tex]The \ fifteenth\ term=C^{15-1}_ {24}(a^3)^{24-15+1}d^{15-1}\\\\The \ fifteenth\ term=C^{14}_{24}(a^3)^{10}d^{14}\\\\The \ fifteenth\ term=\frac{24!}{(24-14)!14!} a^{30}d^{14}\\\\The \ fifteenth\ term=\frac{24!}{10!14!}a^{30}d^{14} \\\\The \ fifteenth\ term=1,961,256 a^{30}d^{14}[/tex]