Fill out the x-y chart. 11. y = log_2 x – 1 X -2 -1 O 1 2 Y C​

​ASAP!!!!

If f (x) = √2x + 4 and g(x) = 1/2(x-4)² then the function is f(g(x)) = √2 * (x-4) * √[1 + 2/[(x-4)²]]

What is function?

An expressiοn, rule, οr law in mathematics that specifies the relatiοnship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functiοns are fundamental fοr cοnstructing physical relatiοnships.

This relatiοnship is typically represented as y = f(x), οr "f οf x," and y and x are related such that fοr each value οf x, there is a specific value οf y. This means that f(x) can οnly have οne value fοr a given x. In set theοry jargοn, a functiοn cοnnects an element x tο an element f(x) in anοther set. The set οf x values is referred tο as the dοmain οf the functiοn, and the set οf f(x) values prοduced by the values in the dοmain are referred tο as the range οf the functiοn.

[tex]f(g(x)) = \sqrt{[2g(x) + 4]}[/tex]

Now we can substitute the expression for g(x):

[tex]f(g(x)) = \sqrt{[2(1/2(x-4)²) + 4]}[/tex]

We can simplify this expression by first expanding the square in the brackets:

[tex]f(g(x)) = \sqrt{[2(x-4)^2 + 4]}[/tex]

Then we can factor out the 2 from the square:

[tex]f(g(x)) = \sqrt{[2(x-4)²] * √[1 + 2/[(x-4)²]]}[/tex]

Simplifying further:

[tex]f(g(x)) = \sqrt{2 * (x-4) * \sqrt{[1 + 2/[(x-4)²]}]}[/tex]

Therefore, [tex]f(g(x)) = \sqrt{2 * (x-4) * \sqrt{[1 + 2/[(x-4)²]}]}[/tex]

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Let's suppose that Tom drives x miles. Then, the total cost of the first plan will be:

C1 = 53.96 + 0.13x

And the total cost of the second plan will be:

C2 = 43.96 + 0.18x

To find how many miles Tom needs to drive for the two plans to cost the same, we need to solve the following equation:

53.96 + 0.13x = 43.96 + 0.18x

Simplifying:

10 = 0.05x

x = 200

Therefore, Tom needs to drive 200 miles for the two plans to cost the same.

The linear equation y = (2/3)x - 3 represents the graph that passes through the points (0, -3) and (3, -1).

What is a linear equation, exactly?

A straight line on a graph is represented by a linear equation, which is a mathematical equation. It is an algebraic equation of the form y = mx + b, where x and y are variables, m represents the line's slope (or gradient), and b represents the y-intercept. The slope m denotes the pace at which y varies in relation to x. In other words, it reflects the slope of the line.

Now,

To determine the equation that represents the graph of a line passing through the points (0, -3) and (3, -1), we can use the slope-intercept form of a linear equation

First, we need to find the slope of the line:

slope = Δy / Δx

slope = (-1 - (-3)) / (3 - 0)

slope = 2/3

Next, we can use one of the given equations and substitute the slope and one of the points to find the y-intercept:

y = mx + b

-3 = (2/3)(0) + b

b = -3

Therefore, the equation is

y = (2/3)x - 3

The equation that represents the graph of a line passing through the points (0, -3) and (3, -1) is y = (2/3)x - 3.

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Using expression (L/3) / (36t) = L / (108t),  the fraction of the total singing time that all three are singing at the same time is L / (108t).

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, and operations that represents a value or a quantity. Expressions can be composed of one or more terms, which are separated by addition or subtraction symbols.

For example, the expression 2x + 3y - 5 represents a value that depends on the values of the variables x and y. The term 2x represents a quantity that is twice the value of x, the term 3y represents a quantity that is three times the value of y, and the term -5 represents a constant value of negative five.

Now,

Let's call the length of the song "L" and the time it takes to sing one line "t". Then, we know that:

Rachel starts singing at t = 0, and she sings for a total of 4L.

Jenny starts singing at t = t, and she sings for a total of 4L.

Angela starts singing at t = 2t, and she sings for a total of 4L.

Since each line of the song is the same length, we can divide the total singing time for each person into three equal parts, one for each line. So, each person sings for a total of 12t.

Now, let's think about when all three people are singing at the same time. This happens during the second line of the first repetition of the song. Rachel is singing the first line, Jenny is singing the second line, and Angela is starting to sing the third line. The total length of time that all three people are singing together is just the length of one line, which is L/3.

Since each person sings for a total of 12t, the total singing time for all three people is 36t. Therefore, the fraction of the total singing time that all three are singing at the same time is:

(L/3) / (36t) = L / (108t)

So, the fraction of the total singing time that all three are singing at the same time is L / (108t).

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The ratio of the number of blueberry bagels to plain bagels sold can be found by dividing the number of blueberry bagels sold by the number of plain bagels sold.

Ratio of blueberry bagels to plain bagels = Number of blueberry bagels sold / Number of plain bagels sold

In this case, the number of blueberry bagels sold is 13 and the number of plain bagels sold is 8.

Ratio of blueberry bagels to plain bagels = 13 / 8

Simplifying this ratio by dividing both numbers by their greatest common factor, we get:

Ratio of blueberry bagels to plain bagels = 1.625 : 1

Therefore, the ratio of the number of blueberry bagels to plain bagels sold is 1.625 : 1.

Answer: a) Erica should choose 2, 3, and 6 to make a whole number and a fraction that have a product close to 1.

2 x 3 x 6 = 36, which is close to 1 when expressed as a fraction: 1/36.

b) (2/a) x (3/b) x (6/c) = 1

c) Multiplying both sides by a, b, and c, we get:

6bc = 2ac

3ac = ab

6ab = bc

Multiplying the three equations together, we get:

(6abc)^2 = (2ac) x (3ab) x (6bc)

216a^2 b^2 c^2 = 36a^2 b^2 c^2

a^2 b^2 c^2 = 1/6

Taking the square root of both sides, we get:

abc = 1/sqrt(6)

So, Erica's whole number is 2 x 3 x 6 = 36, and her fraction is 1/sqrt(6). The product of these is:

36 x 1/sqrt(6) = 6sqrt(6)

Her score is the absolute difference between 6sqrt(6) and 1:

|6sqrt(6) - 1| = 13.97 (rounded to two decimal places).

d) Erica's score for this round is 13.97.

Step-by-step explanation:

The value of variable "x", which makes the equation " 8³ˣ/2²ˣ⁺¹ = 8⁹" true is 10.

We first simplify the left-hand side of the equation using the rules of exponents: which states that if the base of the numerator and denominator is same, then the power can be subtracted,

So, We have : 8³ˣ/2²ˣ⁺¹ = 8³ˣ - ⁽²ˣ⁺¹⁾ = 8ˣ⁻¹ ,

⇒ 8ˣ⁻¹ = 8⁹,

To solve for x, we can use the fact that if two exponential expressions with the same base are equal, then their exponents must be equal as well.

We equate,

⇒ x - 1 = 9,

⇒ x = 10,

Therefore, the value of x that makes the equation true is x = 10.

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In this equation, we have two exponential terms with the same base, 5. To solve for the missing exponents, we can use the laws of exponents, specifically the product law of exponents the missing exponent is 3, and we can write:[tex]5^? x 5^3 = 5^(?+3) = 5^6[/tex]

Using the laws of exponents, we know that when we multiply two exponential expressions with the same base, we add their exponents. Thus:

[tex]5^? x 5^3 = 5^(?+3)[/tex]

Now, we can use the fact that the two expressions on either side of the equation are equal to fill in the missing exponents:

[tex]5^? x 5^3 = 5^(?+3)[/tex]

[tex]5^? x 125 = 5^(?+3)[/tex]

Now we can simplify by dividing both sides of the equation by 5^?:

[tex]125 = 5^3[/tex]

Therefore, the missing exponent is 3, and we can write[tex]5^? x 5^3 = 5^(?+3) = 5^6[/tex]

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The missing term in the equation  [tex]5^? * 5^3 = 5^2[/tex] is x = -1.

The Exponent Product Rule is as follows: [tex]a^{m} * a^{n} = a^{m+n}[/tex] Add the exponents to obtain the product of two numbers with the same base. The Exponent Quotient Rule: [tex]\frac{a^{m} }{a^{n} } = a^{m-n}[/tex]. Subtract the exponent of the denominator from the exponent of the numerator to determine the quotient of two numbers with the same base.

The given equation is [tex]5^? * 5^3 = 5^2[/tex]

Suppose we are considering ? as x, therefore we can rewrite the equation as,

[tex]5^{x} * 5^{3} = 5^{2} \\[/tex]

As the base of the LHS exponent is is same, we can add the exponent

[tex]5^{x +3}[/tex] = [tex]5^{2}[/tex]

Now the base of both sides is equal, so we can compare the exponent.

x + 3 = 2

x = 2 - 3

x = -1

Therefore the missing term is x = -1.

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Complete question:

Find the missing term, [tex]5^? * 5^3 = 5^2[/tex]

the volume of the rectangular prism is 1,080 cubic inches.

Why is it?

The volume V of a rectangular prism is given by the formula:

V = length x width x height

Substituting the given values, we get:

V = 10 inches x 18 inches x 6 inches

Simplifying, we get:

V = 1,080 cubic inches

Therefore, the volume of the rectangular prism is 1,080 cubic inches.

A rectangular prism is a three-dimensional solid shape that has six rectangular faces, where each pair of opposite faces are congruent and parallel to each other. It is also known as a rectangular parallelepiped.

A rectangular prism is characterized by its length, width, and height or depth. The length is the measurement of the longest side of the prism, the width is the measurement of the shorter side, and the height or depth is the measurement of the perpendicular distance between the two faces that are parallel to each other.

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Answer: Let's call the ages of the squirrels C, Celia, and Cecily, and let's represent the number of nuts they took with the variables c, ce, and ce2, respectively.

We know that the total number of nuts is 770, so we can write:

c + ce + ce2 = 770

We also know the ratios of the nuts each squirrel took relative to the others:

Cedric takes 3 nuts for every 4 nuts Celia takes, so we can write c : ce = 3 : 4, or c = (3/4)ce.

Cecily takes 7 nuts for every 6 nuts Celia takes, so we can write ce2 : ce = 7 : 6, or ce2 = (7/6)ce.

Now we can substitute these expressions into the first equation and solve for ce, the number of nuts Celia took:

(3/4)ce + ce + (7/6)ce = 770

Multiplying both sides by 12 to eliminate the fractions, we get:

9ce + 12ce + 14ce = 9240

Simplifying, we get:

35ce = 9240

Dividing both sides by 35, we get:

ce = 264

Now that we know Celia took 264 nuts, we can use the ratios to find how many nuts the other squirrels took:

Cedric took 3/4 as many nuts as Celia, so he took (3/4) * 264 = 198 nuts.

Cecily took 7/6 as many nuts as Celia, so she took (7/6) * 264 = 308 nuts.

Finally, to find how many nuts the youngest squirrel took, we can subtract the nuts taken by the other two squirrels from the total:

c + ce2 = 770 - ce

c + ce2 = 770 - 264 - 198 - 308

c + ce2 = 0

This means that the youngest squirrel did not take any nuts.

Step-by-step explanation:

The probability of picking a red ball is 2/3.

As given in the student question,

The probability that a randomly selected person would be a protestant and at the same time be a democrat or a republican is not given in the problem statement.

Hence, it cannot be determined without further information.

Probability is the branch of mathematics that deals with the study of uncertainty.

It provides a framework for analyzing random events that occur in the real world.

Probability helps us to estimate the likelihood of a particular event occurring. It helps us to make informed decisions when faced with uncertain outcomes.

It plays a critical role in many fields such as science, engineering, economics, and finance.

Probability formula:

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes.

The formula for probability is given by:

P (A) = Number of favorable outcomes/ Total number of outcomes

where P (A) represents the probability of event A.

Example:

Suppose we have a bag containing 10 red balls and 5 blue balls.

The total number of outcomes = 10 + 5 = 15

The number of favorable outcomes = 10P (Red ball) = 10/15 = 2/3

Therefore, the probability of picking a red ball is 2/3.

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Answer:

[tex]v = 8.125 \: {units}^{3} [/tex]

Step-by-step explanation:

Given:

h (height) = 0,5 units

A (base area) = 16,25 units

Find: V (volume) - ?

[tex]v = a(base) \times h [/tex]

[tex]v = 16.25 \times 0.5 = 8.125[/tex]

6 is value of x would prove these lines parallel ​.

Describe a parallel line?

Lines that are always the same distance apart in a plane are said to be parallel. Nothing can cross a parallel line. No matter how far in either direction they may be extended, parallel lines are ones that are equally spaced apart from one another and never cross. For instance, parallel lines are represented by a rectangle's opposing sides.

8x + 6 = 2x + 42

8x - 2x = 42 - 6

 6x = 36

    x = 36/6

     x = 6

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Answer:

  2002.8 mm³

Step-by-step explanation:

You want the volume of a cylinder with radius 5 mm and height 25.5 mm.

The formula for the volume of a cylinder is ...

  V = πr²h

Using the given dimensions, it is found to be ...

  V = π·(5 mm)²(25.5 mm) = 637.5π mm³

  V ≈ 2002.8 mm³

The volume of the cylinder is about 2002.8 cubic millimeters.

The solutions to the equation -x² + 2x = 0 are x = -1 and x = 2, which are the x-intercepts of the graph y = -x² + x + 2

To solve -x² + 2x = 0 using the graph y = -x² + x + 2, we need to first find the x-intercepts. These are the points where the graph intersects the x-axis, which are the solutions to the equation -x² + x + 2 = 0.

We can see from the graph that the vertex of the parabola is at (0.5, 2.25). Since the coefficient of x² is negative, the parabola opens downwards. This means that it intersects the x-axis twice, once on either side of the vertex.

To find the x-intercepts, we can draw a horizontal line at y = 0, which represents the x-axis. This line intersects the parabola at two points: (-1, 0) and (2, 0). These are the solutions to the equation -x² + 2x = 0.

We can also verify our answer by drawing the line y = 2x and seeing where it intersects the parabola. This line passes through the vertex and intersects the parabola at (-1, 3) and (2, 4). These points are symmetrical to the x-axis and have the same y-value, which confirms that they are the x-intercepts.
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We use the normal distribution formula and standard normal distribution table to find the proportion of boys in a school with heights shorter than 67 inches.

To solve this problem, we need to use the normal distribution formula and the standard normal distribution table.

First, we need to convert the height of 67 inches into a standard score or a z-score. The formula to calculate the z-score is:

z = (x - μ) / σ

where x is the height we want to convert, μ is the mean height of the population, and σ is the standard deviation.

So, for x = 67, μ = 70, and σ = 3.5, we have:

z = (67 - 70) / 3.5 = -0.8571

Next, we need to find the area under the standard normal distribution curve to the left of the z-score -0.8571 using the standard normal distribution table. This area represents the proportion of boys in the school who are shorter than 67 inches.

The table gives us that the area to the left of -0.8571 is 0.1950.

Finally, we need to multiply this proportion by the total number of boys in the school to find the expected number of boys who are shorter than 67 inches tall:

Expected number = proportion * total number of boys

Expected number = 0.1950 * 1019

Expected number ≈ 199

Therefore, to the nearest whole number, we can expect about 199 boys in the school to be shorter than 67 inches tall.

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I hope this answer helps.

The first and third quartiles of the given data set are 7.5 and 15.

The median represents the middle number when a dataset is arranged in order. The median is the value that falls in the center when there are an odd number of values. The median is the average of the two center values when there are even more values.

The methods listed below can be used to determine the first and third quartiles of the provided data set:

Step 1: A data collection should be arranged in ascending order:

0 0 1 6 9 9 10 11 11 12 13 14 15 15 21 22

Step 2: Determine the data set's middle.

The median value in the data collection is known as the median. The median is the middle value when the number of values in the data collection is odd. The median is the average of the two middle values when the number of values in the data collection is even.

The data set in this instance contains 16 values, which is an even amount. In order to calculate the average, we select the two middle values:

Median = (11 + 12) / 2 = 11.5

Step 3: Calculate the first quartile (Q1).

In the bottom half of the data set, Q1 represents the median. The median of the bottom half of the data set must first be determined in order to determine Q1.

The lower half of the data set: 0 0 1 6 9 9 10 11

It is an even number since the bottom half of the data set contains 8 values. Consequently, we calculate the average of the two center values:

Median of lower half = (6 + 9) / 2 = 7.5

Therefore, Q1 = 7.5

Step 4: Calculate the third quartile (Q3).

The middle point of the data set's top half is Q3. The median of the top half of the data set must first be determined before we can determine Q3.

The upper half of the data set: 12 13 14 15 15 21 22

Seven values, an odd number, are present in the data set's top half. The median, then, is the midpoint of the range:

The median value for the top half is 15.

Therefore, Q3 = 15

Hence, the first and third quartiles of the given data set are 7.5 and 15, respectively.

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Answer:

(x+2)(2x-9)

Step-by-step explanation:

2x^2 + 4x - 9x - 18

2x(x+2) -9(x+2)

(x+2)(2x-9)

Answer:

The characteristics of the graph of the function f(x) = (x + 1)² + 2 are:

The domain is all real numbers . (option A)

The range is all real numbers greater than or equal to 1 . (option B)

The y-intercept is 3. (option C)

The graph has two x-intercepts. (option E)

The dοmain οf the functiοn f(x) =  {- 3, - 1, 0 2, 4}. Yes, because for each input there is exactly one output.

Suppοse we have an οrdered pair (x, y) then the dοmain οf the functiοn is the set οf values οf x and the range is the set οf values οf y fοr which x  is defined.

Given, The graph represents a relatiοn where x represents the independent variable and y represents the dependent variable.

The οrdered pairs are given by, (- 3, 4), (- 1, 1), (0, - 2), (2, 0), and (4, - 1).

We knοw the dοmain οf the functiοn are all the x cοοrdinates.

Therefοre, The dοmain οf the functiοn f(x) = {- 3, - 1, 0 2, 4}.

Yes, because for each input there is exactly one output.

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If a and c are both less than 0, the following statements must be true:

A. The graph of h will be reflected over the x-axis.

C. The vertex of h will be at (0, c).

Statement A is true because a negative value for "a" causes the parabola to open downwards, which reflects the graph over the x-axis.

Statement C is true because the x-coordinate of the vertex is always -b/2a, which in this case is -0/2a = 0, and the y-coordinate is "c", so the vertex is at (0,c).

Statement B is not necessarily true, as the sign of "c" does not affect the horizontal shift of the graph. If "c" were positive, the graph would shift downwards instead of upwards, but it would still be centered at x=0.

Statement D is not necessarily true, as the sign of "a" determines whether the graph is wider or narrower than the parent quadratic function. A negative value of "a" makes the graph narrower than the parent function, while a positive value of "a" makes it wider.

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The price of the house at the end of 2008 will be 39,60,000

We must determine the price following each rise in order to determine the cost of the house at the end of 2008.

First of all, in 2004 the price jumped by 10%.

10% of 30,00,000 = 0.1 x 30,00,000 = 3,00,000

As a result, the house's new price in 2004 was:

30,00,000 + 3,00,000 = 33,00,000

The price then rose by 20% in 2008.

20% of 33,00,000 = 0.2 x 33,00,000 = 6,60,000

The home's total price at the end of 2008 was therefore: 33,00,000 + 6,60,000 = 39,60,000.

As a result, the house cost 39,60,000 at the end of 2008.

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Yes, that’s correct! A sphere's volume is equivalent to a cylinder's volume by a factor of two-thirds whose height and diameter match the sphere's diameter

The formula below can be used to calculate a sphere's volume:

V = 4/3πr³

The points on the three-dimensional surface of a sphere are all equally far from the object's centre.

A cylinder is a three-dimensional shape made up of two parallel bases joined together by curves.

A sphere is viewed by mathematicians as a two-dimensional closed surface encased in three-dimensional space that is Euclidean. They distinguish between spheres and balls, which are three-dimensional manifolds with boundaries that encompass the volume encompassed by the sphere.

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A one-sample t-test was conducted to determine if the temperature increased in the first week of October 2019 compared to the average temperature from the previous 10 years. The result showed a p-value of 0.032, indicating a significant increase in temperature.

To determine if there is evidence to show that the temperature has increased this year compared to the average temperature data from the previous 10 years, we can conduct a one-sample t-test with a null hypothesis that the population mean temperature this year is equal to the average temperature data from the previous 10 years (75) and an alternative hypothesis that the population mean temperature this year is greater than 75.

Using a statistical software, the calculated t-value is 2.17 with a corresponding p-value of 0.032. Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is evidence to show that the temperature has increased this year compared to the average temperature data from the previous 10 years. The p-value of 0.032 indicates that the probability of observing a sample mean temperature as extreme as 79.29 (the calculated sample mean temperature this year) or greater, assuming that the population mean temperature is equal to 75, is 0.032.

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The farmer can make at most 3 complete picture frames with some usable board left over after subtracting the scratched portion and dividing the usable length by the length needed for each picture frame.

To find the amount of usable board, we need to subtract the scratched portion from the total length of the board:

101/12 - 23/8

Converting to a common denominator, we get:

122/12 - 19/8 = 976/96 - 228/96 = 748/96

Simplifying, we get:

72/96 feet

Now, we can divide this usable length by the length needed for each picture frame:

722/96 ÷ 1 2/3

Converting the mixed number to an improper fraction, we get:

722/96 ÷ 5/3 = 748/96 ÷ 5/3 = 748/96 x 3/5 = 3.9

Therefore, the farmer can make at most 3 complete picture frames with some usable board left over.

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Answer:

The rate of change is 400

The altitude increases by 400 feet every minute.

Step-by-step explanation:

We Know

x = the number of minutes the balloon rises.

y = altitude of the balloon.

To find the Rate of change (slope), we can use rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0, 150) (1, 550)

We see the y increase by 400 and the x increase by 1, so

The rate of change is 400

The altitude increases by 400 feet every minute.

Answer:

A. y=[x+4]-2

Step-by-step explanation: