2. Write an equation that represents the following situation

Starting value = 200
Rate = 2.5% decay per year
Years = 5 years​

Step-by-step explanation:

(f○g)(x) = f(g(x))

so, we use the expression of g(x) as the "x" in f(x).

(f○g)(x) = f(g(x)) = 3(x² + 3) - 1 = 3x² + 9 - 1 = 3x² + 8

so,

(f○g)(3) = 3×3² + 8 = 27 + 8 = 35

check :

g(3) = 3² + 3 = 9 + 3 = 12

f(g(3)) = f(12) = 3×12 - 1 = 36 - 1 = 35

correct.

Answer: −1.3571428 (with a repeating bar over .3571428)

Step-by-step explanation:

There are many tools available to calculate the line of best fit, including Excel, R, and Python. These tools provide the best equation that approximates the data

To determine which equation could be used as a line of best fit to approximate the data in a scatter plot, we need to look for the equation that closely follows the general trend of the data. The line of best fit is the straight line that best represents the data on the graph.

One common method for finding the line of best fit is through linear regression analysis. This involves calculating the slope and intercept of the line that best fits the data. The equation for a line is y = mx + b, where m is the slope and b is the y-intercept.

In general, the equation that could be used as a line of best fit depends on the data on the scatter plot. However, we can determine the best equation by looking at the trend of the data. If the data shows a positive trend, we need to choose an equation with a positive slope. If the data shows a negative trend, we need to choose an equation with a negative slope.

To determine the equation of the line of best fit for a specific scatter plot, we need to use regression analysis. and allows us to make predictions based on the data.

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Therefore, the length of the side x is approximately 10.76.

A right-angled triangle, also known as a right triangle, is a type of triangle that has one of its angles measuring exactly 90 degrees. The other two angles in a right triangle are acute angles, which means they are less than 90 degrees. The side opposite to the right angle is called the hypotenuse, and it is the longest side of the triangle. The other two sides of the right triangle are called legs, and they are adjacent to the right angle. The Pythagorean theorem, which states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of its hypotenuse, is a fundamental concept in the study of right triangles. Right triangles have many practical applications in geometry, trigonometry, and physics.

In a right triangle, the sum of the measures of the two acute angles is always 90 degrees. Therefore, the third angle in this triangle is:

90 - 34 = 56 degrees

Now, we can use the trigonometric ratios to find the length of the side x.

We know that the tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side. Therefore:

[tex]tan(34) = x/18[/tex]

To solve for x, we can multiply both sides by 18:

[tex]18 tan(34) = x[/tex]

Using a calculator, we can find that:

18 tan (34) ≈ 10.76.

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Using division, we can prove that there are models that we can use to prove 7 divided by 2 is = 7/2.

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many groups will be created, for instance, if a sports event requires that 30 students be divided into groups of 5 students. The division operation makes it simple to tackle such issues. Divide 30 by 5 in this case. The outcome is 30 x 5 = 6. There will thus be 6 groups, each with 5 pupils. By multiplying 6 by 5, which yields the initial figure of 30, you can confirm this value.

Here in the question,

We have to model to find 7 divided by 2 = 7/2.

For the two math classes, 7 pizzas have been delivered.

Half of the first pizza is distributed to each class.

A half of the second pizza is distributed to each class.

Third pizza, cut in half, with half going to each class.

Continue until each class receives 7 halves, or 7/2, of the pizzas that were delivered.

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The labelled parts of the circle include:

A secant of a circle is a line that intersects the circle in two distinct points. In other words, a secant is a line that cuts through a circle. The length of a secant segment between the two points of intersection with the circle is called the length of the secant.

An inscribed angle is the angle formed in the interior of a circle by the intersection of two chords on the circle.

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Image transcribed:

CIRCLES ESCAPE Challenge

Directions A circle is given to the left. Parts of this circle are partially named below. Complete the names by dragging and placing the letters over the empty spaces. Though there could be more than one answer, each letter tile can only be used once

Center

Radius

Diameter

Chord

Secant

Tangent

Central Angle

Inscribed Angle

Minor Arc

Major Arc

The value of x for the intersecting chords is equal to 44°

The property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

x = (124° - 36°)/2

x = 88°/2

x = 44°

Therefore, the value of x for the intersecting chords is equal to 44°.

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The surface area of the composite figure is 944 cm².

What is the surface area of a cuboid?

Surface area of a cuboid is (lb+lh+bh) where l,b,h are length, breadth and height of the cuboid.

To find the surface area of the composite figure, we need to calculate the surface area of both cuboids and then subtract the area of any faces that are shared by both cuboids.

Given dimension of first cuboid is 14 cm × 8 cm × 2 cm and dimension of the second cuboid is 8 cm × 6 cm × 4 cm.

Surface area of the first cuboid:

Area of the top and bottom faces = 2(14 x 8) = 224 cm²

Area of the front and back faces = 2(14 x 2) = 28 cm²

Area of the left and right faces = 2(8 x 2) = 32 cm²

Total surface area of the first cuboid = 2(224) + 2(28) + 2(32) = 576 cm²

Surface area of the second cuboid:

Area of the top and bottom faces = 2(8 x 6) = 96 cm²

Area of the front and back faces = 2(8 x 4) = 64 cm²

Area of the left and right faces = 2(6 x 4) = 48 cm²

Total surface area of the second cuboid = 2(96) + 2(64) + 2(48) = 416 cm²

Now we need to identify the faces that are shared by both cuboids. The first cuboid has a bottom face that is the same size as the top face of the second cuboid (6 x 4). The surface area of this shared face is 48 cm².

Therefore, the surface area of the composite figure is total surface area of the first cuboid + Total surface area of the second cuboid - Area of shared face

= 576 + 416 - 48

= 944 cm²

So the surface area of the composite figure is 944 cm².

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The answer is (A) The Ratio Test says that the series converges absolutely.

What is the ratio test?

The Ratio Test is a test used to determine whether an infinite series converges or diverges. It involves taking the limit of the absolute value of the ratio of the (n+1)th term to the nth term as n approaches infinity. If the limit is less than 1, then the series converges absolutely.

We have:

[tex]|a_{n+1}/a_{n}| = |(e^(n+7)*sqrt(n+3)/((n+4)!)) / (e^(n+6)*sqrt(n+2)/((n+3)!))|[/tex]

[tex]|a_{n+1}/a_{n}| = e(sqrt(n+3)/sqrt(n+2)) * (n+3)/(n+4)[/tex]

We want to compute:

[tex]L = lim n- > infinity |a_{n+1}/a_{n}| = lim n- > infinity e(sqrt(n+3)/sqrt(n+2)) * (n+3)/(n+4)[/tex]

We can see that the exponent of e goes to 1 as n goes to infinity, and (n+3)/(n+4) goes to 1 as n goes to infinity. Therefore, L = 1.

Since L < 1, by the Ratio Test, the series converges absolutely.

Hence, the answer is (A) The Ratio Test says that the series converges absolutely.

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Answer:

The answer is C unlikely and likely

Step-by-step explain

the is 50% chance of getting likely or unlikely

Answer:

Step-by-step explanation:

A 50% probabilty is interpreted as being equally ikely and unlikely.

The correct answer is: The theoretical probability, P(blue), is 25%, and the experimental probability is 30%

Theoretical probability is a concept in mathematics and statistics that refers to the likelihood or chance of an event occurring based on mathematical reasoning and analysis. Theoretical probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes in a given situation or experiment. It is based on the assumption that each outcome is equally likely to occur.

The theoretical probability of pulling a blue marble from the bag is the number of blue marbles divided by the total number of marbles:

P(blue) = 10/40 = 1/4 = 25%

The experimental probability of pulling a blue marble from the bag is the number of times a blue marble was pulled divided by the total number of trials:

Experimental probability of pulling a blue marble = 12/40 = 3/10 = 30%

We can see that the experimental probability of pulling a blue marble is slightly higher than the theoretical probability, which is expected since this is based on a limited number of trials and chance variation can occur. However, as the number of trials increases, the experimental probability should converge to the theoretical probability.

The correct answer is: The theoretical probability, P(blue), is 25%, and the experimental probability is 30%.

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Answer: Reread the lesson and then you will figure it out

Step-by-step explanation:

Answer:

A/First picture

Step-by-step explanation:

The line touches the y axis at 3, as indicated by the +3 in the equation. In addition, the -1/2x indicated a downwards line.

Answer:

the first photo

Step-by-step explanation:

I hope this helps

To solve the problem, we need to use the given function f(x) = 4 + z(0.25) where x is the amount of 25% orange juice drink added and z is the amount of 100% orange juice drink added.

We know that initially 4 gallons of pure juice are present. So, the total amount of juice in the mixture is 4 + x gallons.

When we add 2 gallons of 25% orange juice drink, x = 2 and z = 0. So, using the function f(x), we get:

f(2) = 4 + z(0.25)

    = 4 + 0(0.25)

    = 4

Therefore, the concentration of orange juice in the drink after adding 2 gallons of 25% orange juice drink is 4%, expressed as a percent but without the percent sign.

Answer: 4

Lily increased the amount of protein she eats by 12.5% by eating every day from 48 g to 54 g.

How to calculate percentage for the given problem?

To find the percentage increase in the amount of protein that Lily eats, we can use the following formula:

Percentage increase = ((new value - old value) / old value) x 100%

Using this formula and plugging in the values given in the problem, we get:

Percentage increase = ((54 - 48) / 48) x 100%

Percentage increase = (6 / 48) x 100%

Percentage increase = 0.125 x 100%

Percentage increase = 12.5%

Therefore, Lily increased the amount of protein she eats by 12.5%.

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Answer:

1

Step-by-step explanation:

Answer:

There are 10 possible digits that could appear on the license plate: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Half of these digits (1, 3, 5, 7, and 9) are odd.

Since there are three digits on the license plate, there are 10x10x10 = 1000 possible license plates.

To find the probability that the last digit is odd, we need to find the number of license plates where the last digit is odd and divide by the total number of possible license plates:

Number of license plates where last digit is odd = 10x10x5 = 500 (since there are 5 odd digits to choose from for the last digit)

Total number of possible license plates = 10x10x10 = 1000

So the probability of selecting a license plate at random where the last digit is an odd number is:

500/1000 = 0.5 or 50%

Hope This Helps!

The number οf hοurs fοr Shandra wοrking tο wash car is 2 hοurs.

The number οf hοurs fοr Shandra wοrking tο walking dοgs is 9 hοurs.

Mathematical expressiοn is defined as the cοllectiοn οf the numbers variables and functiοns by using οperatiοns like additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Given that;

Shandra is wοrking twο summer jοbs, making $9 per hοur washing cars and $8 per hοur walking dοgs.

Last week Shandra wοrked a tοtal οf 11 hοurs.

Tοtal earned = $90

Nοw,

Tοtal number οf hοurs tο wash car = x

Tοtal number οf hοurs tο walk dοgs = y

Sο, We can fοrmulate;

⇒ 9x + 8y = $90  ... (I)

And, x + y = 11   .. (ii)

Sοlve equatiοn (i) and (ii) we get;

x = 2 hοurs and y = 9 hοurs

Sο, The number οf hοurs fοr Shandra wοrking tο wash car is 2 hοurs.

The number οf hοurs fοr Shandra wοrking tο walking dοgs is 9 hοurs.

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The complete statement is: Tina can select and answer the essay questions on her test in 10 ways.

Tina has to answer any 2 of 5 questions, which means she needs to choose 2 questions out of the 5 available questions.

The number of ways to choose r items from a set of n items is given by the combination formula:

C(n,r) = n! / (r!(n-r)!)

In this case, n = 5 (the total number of questions) and r = 2 (the number of questions that Tina needs to choose).

So we can plug in these values to get:

C(5,2) = 5! / (2!(5-2)!)

C(5,2) = (5 x 4 x 3 x 2 x 1) / [(2 x 1) x (3 x 2 x 1)]

C(5,2) = (5 x 4) / (2 x 1)

C(5,2) = 10

Therefore, Tina can select and answer the essay questions on her test in 10 ways.

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Therefore, Andrey's score was 65.4. Therefore, Susan's score was 79.

Standard deviation is a statistical measure that represents the amount of variation or dispersion in a set of data values. It measures the average distance of each data point from the mean of the data set. A low standard deviation indicates that the data points tend to be close to the mean, while a high standard deviation indicates that the data points are more spread out. It is calculated by taking the square root of the variance, which is the average of the squared differences of each data point from the mean. Standard deviation is commonly used in fields such as finance, engineering, and psychology to analyze and compare data sets.

Here,

a. To find Andrey's score, we need to use the formula:

z = (x - μ) / σ

where z is the number of standard deviations from the mean, x is the score, μ is the mean, and σ is the standard deviation.

Andrey was told that he scored 1.2 standard deviations below the mean, so we have:

z = -1.2

μ = 75

σ = 8

Plugging these values into the formula, we get:

-1.2 = (x - 75) / 8

Multiplying both sides by 8, we get:

-9.6 = x - 75

Adding 75 to both sides, we get:

x = 65.4

b. Similarly, to find Susan's score, we have:

z = 0.5

μ = 75

σ = 8

Plugging these values into the formula, we get:

0.5 = (x - 75) / 8

Multiplying both sides by 8, we get:

4 = x - 75

Adding 75 to both sides, we get:

x = 79

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"The spread of the data distribution for Lake Mockingbird is 5 inches bigger than the spread of the data distribution for Lake Warbler," is the answer to question 2.

The graphs do not support this statement since the difference in spread between the two lakes is not represented as 5 inches. The right answer to question 1 is B: "The spread of the data distribution for Lake Mockingbird is approximately 40% higher than the spread for Lake Warbler." This is due to the fact that the data distribution of the Lake Mockingbird is around 60 inches (from 5 to 65), whereas the data distribution of the Lake Warbler is approximately 43 inches (from 2 to 45). The difference between the two ranges is approximately 60 - 43 = 17. inches. From 43 to 60, the percentage rise is around 39.5%, which is close to 40%. The correct answer to question 3 is B: "The distribution of Lake Mockingbird reveals a center that is 3 inches greater than the distribution of Lake Warbler." This assertion is false since the graphs do not show the center of each distribution and cannot be established with the information supplied. Based on the data in the graphs, the other claims are correct.

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The possible length, width, and perimeter for Small cage's floor is 4 feet, 3 feet and 14 feet respectively; for Medium cage's floor is 12 feet, 2 feet and 28 feet respectively and for Large cage's floor is 18 feet, 2 feet and 40 feet respectively.

What is perimeter?

Whether it be a two-dimensional shape or a one-dimensional length, a perimeter is a closed path that contains, surrounds, or delineates it.

We are given the floor areas of each cage.

For Small cage:

Area is given as 12 square feet which is a product of length and width.

So, here length can be 4 feet and width can be 3 feet.

Now, we get the perimeter as

⇒ Perimeter = 2 * (Length + width)

⇒ Perimeter = 2 * (4 + 3)

⇒ Perimeter = 2 * 7

⇒ Perimeter = 14 feet

For Medium cage:

Area is given as 24 square feet which is a product of length and width.

So, here length can be 12 feet and width can be 2 feet.

Now, we get the perimeter as

⇒ Perimeter = 2 * (12 + 2)

⇒ Perimeter = 2 * (14)

⇒ Perimeter = 28 feet

For Large cage:

Area is given as 36 square feet which is a product of length and width.

So, here length can be 18 feet and width can be 2 feet.

Now, we get the perimeter as

⇒ Perimeter = 2 * (18 + 2)

⇒ Perimeter = 2 * (20)

⇒ Perimeter = 40 feet

Hence, the required solution has been obtained but there are many other combinations possible.

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Answer:

The tip was $14

Answer:

Step-by-step explanation:

(2+3) x 3 + 8/2 = 5 X 3 + 8/2 = 15 + 4 = 19

The value of the functions are;

1. (f+g(x)) = -x² -x + 1,  (f-g(x)) = -5x²+ 5x - 7

2. (f+g(x)) = 6x² - 4x + 6,  (f-g(x)) = 2x² - 6x + 10

3. (f+g(x)) = 3√m . √4, (f-g(x)) = √m· √4

4. (f+g(x)) = 7x² - 3x - 5, (f-g(x)) = x² + 3x + 5

It is important to note that functions are described as an equation or expression showing the relationship between two variables.

From the information given, we have the functions

1.

f(x) = -3x² + 2x - 3

g(x) = 2x² - 3x + 4

To add the functions, we have;

(f+g(x)) =  -3x² + 2x - 3 + 2x² - 3x + 4

collect the like terms and add

(f+g(x)) = -x² -x + 1

(f-g(x)) =  -3x² + 2x - 3 - 2x² +3x - 4

collect the like terms and subtract

(f-g(x)) = -5x²+ 5x - 7

2. f(x) = 4x² - 5x + 8

g(x) = 2x² + x - 2

(f+g(x)) = 4x² - 5x + 8 + 2x² + x - 2

(f+g(x)) = 6x² - 4x + 6

(f-g(x)) =4x² - 5x + 8 -  2x² - x +2

subtract the values

(f-g(x)) = 2x² - 6x + 10

3. f(x) = 2√m

g(x) = 3√4m

(f+g(x)) = 2√m + √m. √4

(f+g(x)) = 3√m . √4

(f-g(x)) = 2√m -√m. √4

(f-g(x)) = √m· √4

4. f(x) = √16x^4

g(x) = 3x² - 3x - 5

(f+g(x)) = √16x^4 +  3x² - 3x - 5

find the square root

(f+g(x)) = 7x² - 3x - 5

(f-g(x)) =√16x^4 -  3x² + 3x +5

(f-g(x)) = x² + 3x + 5

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The linear inequality for the shaded region with slope [tex]-4[/tex] is:

[tex]y < -4x+4[/tex]

In mathematics, a linear inequality is an inequality involving a linear function in one or more variables. It describes a region in the coordinate plane that satisfies the inequality.

In mathematics, the slope is a measure of the steepness of a line. It describes how much a line rises or falls as we move from left to right along it.

According to the given information

To write the linear inequality for the graph passing through points [tex](0,4)[/tex] and [tex](1,0)[/tex], we need to find the equation of the line first.

The slope of the line passing through these two points is:

[tex]m =(y_{2} -y_{1} )/(x_{2} -x_{1} )\\ = (0-4)/(1-0)\\ = -4[/tex]

Using the slope-intercept form of a linear equation, [tex]y = mx +b[/tex], where m is the slope and b is the y-intercept, we can find the equation of the line passing through these two points:

[tex]y = -4x+4[/tex]

Now, to write the linear inequality for this line, we need to determine which side of the line is shaded. We can use the test point [tex](0,0)[/tex] to check which side of the line contains the solutions to the inequality.

If we plug in [tex](0,0)[/tex] into the equation [tex]y = -4x+4[/tex], we get:

[tex]0= -4(0) +4\\0 = 4[/tex]

Since [tex]0[/tex] is not less than [tex]4[/tex], the point [tex](0,0)[/tex] is not a solution to the inequality. Therefore, we need to shade the side of the line that does not contain the origin [tex](0,0)[/tex].

The linear inequality for the shaded region is:

[tex]y < -4x +4[/tex]

Therefore any point below the line [tex]y < -4x +4[/tex] satisfies this inequality.

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[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{P = 2 ( x +y)}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf\underline{Perimeter_{(rectangle) } = 2 ( Height +Base)\: unit}\\[/tex]

Where-

As per question, we are given that -

We are asked to find out the value of perimeter for the given rectangle. Now that we have all the required values, so we can put them into the formula and solve for the perimeter -

[tex] \:\:\:\:\:\:\longrightarrow \sf\underline{Perimeter_{(rectangle) } = 2 ( Height +Base)\: unit}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf Perimeter_{(rectangle) } = 2\bigg(10+9\bigg)\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf Perimeter_{(rectangle) } = 2 \times 19\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{Perimeter_{(rectangle) }=38 \:ft }\\[/tex]