1) f(x) = x(x − 4)³(x+4)²
x-intercepts:
Positive or Negative
Even or Odd
End Behavior:

1. Using the Pythagoras theorem, the area of the rectangle RSTW is 168 units².

2. Using the Pythagoras theorem, the measure of line segment ST is 48 units.

What is Pythagoras Theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

The diagonal SW measures = 25 units

The breadth ST measures = 24 units.

Applying the Pythagoras theorem -

(Hypotenuse)² = (Base)² + (Perpendicular)²

Substituting the values in the equation -

(SW)² = (ST)² + (WT)²

(25)² = (24)² + (WT)²

(WT)² = (25)² - (24)²

(WT)² = 625 - 576

(WT)² = 49

WT = √49

WT = 7 units

The length WT measures = 7 units

The formula for the area of the rectangle is -

Area = Length × Breadth

Area = WT × ST

Area = 7 × 24

Area = 168 units²

Therefore, the area of the rectangle is obtained as 168 units².

The line segment SZ measures = 25 units

According to the properties of rectangle the diagonals bisect each other.

So, the measure of SW = 2(SZ) = 50 units

The length WT measures = 14 units

Applying the Pythagoras theorem -

(Hypotenuse)² = (Base)² + (Perpendicular)²

Substituting the values in the equation -

(SW)² = (ST)² + (WT)²

(50)² = (ST)² + (14)²

(ST)² = (50)² - (14)²

(ST)² = 2500 - 196

(ST)² = 2304

ST = √2304

ST = 48 units

Therefore, the breadth ST measures = 48 units.

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Answer:

40% decrease

Step-by-step explanation:

since it is 100 it is easy to convert to a percentage. 100-60=40 so you have a 40% decrease

Answer:

72ft

Step-by-step explanation:

Area of one square = 54ft^2/6 = 9ft^2

The side of the square is the square root of the area, so the side length of one square is

√9ft^2 = 3ft.

each square has a perimeter of

4*3ft = 12ft.

So the perimeter of all six squares is

12ft * 6 = 72ft

According to the given information in the question answer is  250.

Any decimal number is rounded down to the closest hundredth by the term "to the nearest hundredth." A hundredth is 1/100 or 0.01 in decimal form. For instance, increasing 2.167 to the closest tenth yields 2.17.

In this exercise, we must round the supplied number up to the nearest hundred, making it 10.2719. We must add two more decimal places to this number in order to round it to the nearest hundreds. Additionally, we saw that all of the numbers following the second decimal place are fewer than five, therefore they can be ignored and the result is 10.27.

Using the following formula, you can determine this:

x = (100 * 305) / 122

Where x is the original number and 122 is 100 + 22 (the 100 representing the original value and 22 representing the increase of 22%).

x = (100 * 305) / 122 = 250

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The surface area of the interior of the box is the total area of the interior walls of the box.

This can be calculated by subtracting the area of the 5 unit square removed from the total area of the original 20 by 30 unit rectangular sheet of cardboard. This gives us an area of 450 units. To calculate the area of the interior walls, we need to multiply the length and width of the remaining rectangle. This gives us a length of 15 units and a width of 25 units, which gives us a total area of 375 units. Therefore, the surface area of the interior of the box is 375 square units. We can calculate this using the formula A = L x W, where A represents the area, L represents the length and W represents the width.

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The number of classes in the frequency table given below is; 5 classes

We are given the classes of the frequency table as;

23 - 24

25 - 26

27 - 28

29 - 30

31 - 32

Now, we see from the class intervals that there are a total of five classes because each class interval has a frequency of occurrence as seen in the given frequency table.

The frequencies for each class interval is as follows;

7, 2, 6, 4, 1

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The new coordinate of Q after a rotation of 90° is (10, -5)

Rotation simply means turning

In order to answer this question, you need to know the rotation rule  for  90° about the origin.

If a point P, whose position vector is (x,y), is rotated 90° counterclockwise rotation about the origin, the position of the image P' is (-y, x).

From the graph, the initial coordinate of Q is (-5, -10).

Thus, the new coordinate of Q will be (10, -5)

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Answer:

To solve the equation Z - 2/5=1/3, we need to get Z alone on one side of the equation.

First we add 2/5 to both sides of the equation to get

Z - 2/5 + 2/5 = 1/3 + 2/5

Z = 1/3 + 2/5

To combine the fractions on the right side of the equation, we need to find a common denominator.

The common denominator of 1/3 and 2/5 is 15

So we can convert 2/5 to 9/15

Z = 1/3 + 9/15

Now we can add the fractions

Z = 12/15 + 9/15

Z = 21/15

So the solution to the equation is Z = 21/15

Step-by-step explanation:

answer:

Max =$131,250

Sherry=$140,000

Duane=$78,750

Step-by-step explanation:

Max will receive 3/8 ×$350,000=$131,250

Sherry will receive 2/5 × $350,000=$140,000

Duane will receive $350,000-$(131,250+140,000)

$350,000-$271,250=$78,750.

The level of measurement of the data can be given as follows:

Interval or ratio.

There are four levels of measurement for the data, given as follows:

The measures of central tendency for each level are given as follows:

For this problem, we have the arithmetic mean, meaning that the level of measurement can be either interval or ratio.

The problem asks for the level of measurement of the data.

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Answer:

Choice C. is the answer

Step-by-step explanation:

greetings !!

just following the series the

If any questions and unclear ideas tag on comment box.

Hope it helps!!!

The solutions are 150, 2.5, 39 and 101. The solutions have been obtained using the arithmetic operations.

What are arithmetic operations?

In all, there are four basic mathematical operations which are applicable for all the real number. The operations are as follows:

1.Addition(‘+’) operation which gives the sum of the numbers.

2.Subtraction(‘-’) operation which gives the difference of the numbers.

3.Multiplication(‘×’) operation which gives the product of the numbers.

4.Division(‘÷’) operation which gives the quotient of the numbers.

1. The sum of 6 and the square of 12

The square of 12 = 12*12 = 144

Sum of 6 and 144 = 6 + 144 = 150

2. The quotient of 30 and the sum of 5 and 7

The sum of 5 and 7 = 5 + 7 = 12

The quotient of 30 and 12 = 30 ÷ 12 = 2.5

3. The difference of 4 cubed and 25

The cube of 4 = 4*4*4 = 64

The difference of 64 and 25 = 64 - 25 = 39

4. 5 more than the product of 12 and 8

The product of 12 and 8 = 12*8 = 96

5 more than 96 = 5 + 96 = 101

Hence, the solutions are 150, 2.5, 39 and 101.

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a) The radius of the area of the oil leakage is described by R = √(112.345 · t).

b) The time related to a radius 1 kilometers is approximately 8901.153 hours.

In this problem an oil tanker has a leakage on ocean surface, the consequence of such event is a contaminated area of circular form, whose formula is described below:

A = π · R²

Where:

And the area density (σ), in liters per square meter, is defined by following formula:

V = σ · A

Where V is the volume leaked, in liters, whose formula is described:

V = V' · t

Where:

Part A - The resulting expression in terms of time is shown below:

V = σ · A

V' · t = σ · π · R²

R = √[(V' · t) / (σ · π)]

(V' = 3000 L / h, σ = 4 / 5 L / m²)

R = √[(3000 · t) / (8.5π)]

R = √(112.345 · t)

Part B - If we know that R = 1000 m, then the time needed is:

1000 = √(112.345 · t)

t = 8901.153 h

Statement is incomplete. Complete form is shown below:

Oil is leaking from an oil tanker at the tanker of 3000 liters per hour. 8 liters of oil spread out over 10 square meter of ocean surface. A circular oil slick forms.

a) Express the radius R of the oil slick as a function of the time t (in hours) the tank has been leaking.

b) After how many hours will the oil slick have radius 1 kilometer?

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The angle ∠G will be 140° for the given curve.

An arc is a section of a circle's or curve's boundary in mathematics. It is additionally known as an open curve. The circumference also referred to as the perimeter, is the measurement around a circle that defines its edge.

Given that the angle ∠I is equal to 70°. The value of angle G will be calculated by the angle of the arc theorem.

One-half the size of the central angle is the size of an angle that is inscribed in a circle. Congruent inscribed angles are those that intersect the same arc.

∠I = ( 1 / 2 ) x ∠G

∠G = 2 x ∠I

∠G = 2 x 70

∠G = 140

Hence, the angle ∠G will be 140.

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Answer: a) 8:6

              b) 8:14

Step-by-step explanation:

You got the answer correct for a but you have to switch the numbers around because the ratio of red apple to green apples is 8:6

The coordinates of the image of the point Q is Q'(3, 6).

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

From the given graph, we have point Q(-4, 4).

Here the point is translated.

After translation, the original figure is shifted from a place to another place without affecting it's size.

The rule of translation is given as the point (x, y) is translated as (x + 1, y + 2).

So the given point is (-4, 4).

(-4, 4) after translation becomes by the definition (-4 + 1, 4 + 2).

So the required point is (-3, 6).

Hence the image of point Q is (-3, 6).

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Your question is incomplete, Probably, the correct graph for the question is given below.

The correct option regarding the slope of the linear function at point P is given as follows:

C. 0.333.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The line in this problem is defined as follows:

y = x/3.

Meaning that:

The slope is the same for each point on the curve, hence the correct option is given by option C.

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The dimensions of the tennis court are 42 feet by 114 feet.

Let the width of the tennis court be x feet.

We can use the formula for perimeter to solve this problem. The perimeter of a rectangle is equal to 2 times the length plus 2 times the width.

2(2x + 30) + 2x = 228

4x + 60 = 228

4x = 168

x = 42

The length of the tennis court is 2x + 30 = 2(42) + 30 = 114 feet.

The dimensions of the tennis court are 42 feet by 114 feet.

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The annual percentage rate for this credit card account is 15.75%.

The annual percentage rate (APR) is the actual annual cost of borrowing money.

Before applying the APR on the account balance, we determine the monthly percentage rate (MPR) by dividing the APR by 12.

Given the interest in dollars and the principal or account balance, the APR can be computed by dividing the interest by the account balance and multiplying it by 12.

Principal        $1,565.89       $1,026.44

Interest                20.55               13.47

Payment           560.00

End of the month balance 1,026.44

Interest rate (MPR) = 1.31235% ($20.55/$1,565.89 x 100)

Annual percentage rate = 15.75% (1.31235% x 12)

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What is the annual percentage rate?

The distance of the town from the base of the cliff  is; 62.42 ft

The 6 trigonometric ratios are;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/ adjacent

sec θ = 1/cos θ

cosec θ = 1/sin θ

cot θ = 1/cot θ

We are given the angle of depression as 10 degrees. By definition of alternate angles, the angle the hypotenuse formed will make with the base of the town is 10 degrees.

Since the height from the cliff to the town is 354 ft, then we can use trigonometric ratio to find the distance of the town from the base of the cliff as;

354/adjacent = tan 10

adjacent = 354 * tan 10

adjacent = 62.42 ft

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A function that represents the transformation include the following: B. g(x) = (x + 4) + 3.

In Mathematics, the translation of a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image or function.

Conversely, the translation a geometric figure or graph upward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image or function.

By translating the pre-image vertically upward by 3 units and horizontally left by 4 units, the function becomes;

f(x) = x

f(x) → g(x) = (x + 4) + 3.

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The product meaning in maths is a number that we get to by multiplying two or more other numbers together.

What is Product?

In mathematics, a product is the outcome of multiplying two or more numbers together.

Let us consider the scenario.  A person had to buy 4 cupcakes. Each cupcake costs $5.

To calculate the total amount he needs to pay at the checkout counter, add the cost of each cupcake 4 times (as he needs to buy 4 cupcakes).

So, the answer will be -

5 + 5 + 5 + 5 = 20

If he needed 10 cupcakes, he would have to add the cost 10 times.

This is where the concept of multiplication and product can help him.

He can find the cost as -

4 times 5 or 4 × 5,

He can skip count by 5, four times and get the answer as 20.

Therefore, product is repetition for the sum of numbers.

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The composition with rotation to map ΔABC to ΔA'B'C' is;

Reflection across the y-axis and 270 degrees counterclockise rotation about the origin

A rotation is defined as a type of transformation that takes each point in a figure and rotates it to a specific number of degrees around a given point.

Now, the coordinates of triangle ABC from the graph are;

A(-8, -2)

B(-6, 3)

C(-5, -1)

The coordinates of triangle A'B'C' from the graph are;

A(-2, -8)

B(3, -6)

C(-1, -5)

Now, the transformation rule for reflection across the y -axis is (x, y) → (-x, y) .

Finally rotation 270 degrees counterclockwise will produce;

(-x, y) → (y, x)

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Answer:

43.7 ft

Step-by-step explanation:

h= height of the building

tan(17) = h/143

h = tan(17) x 143 = 43.7 ft

Answer:

a) To estimate the probability that the server will earn at least $800 in tips, we need to use the cumulative distribution function (CDF) of the normal distribution, since the mean and standard deviation of the tips are given. The CDF of the normal distribution with mean μ and standard deviation σ is given by F(x) = P(X <= x) = (1/2)(1 + erf((x-μ)/(σ * sqrt(2)))

We can use this formula to find the probability that the server will earn at least $800 in tips. We know that the mean of the tips is $10.70, and the standard deviation is $6.70. Therefore, we can calculate the CDF of the normal distribution with μ = $10.70 and σ = $6.70.

P(X >= 800) = 1 - P(X <= 800) = 1 - F(800)

b) To find out how much the server earns on the best 10% of such weekends, we need to find out what the 90th percentile of the distribution is. We can use the inverse cumulative distribution function (ICDF) of the normal distribution to find this. The ICDF of the normal distribution with mean μ and standard deviation σ is given by x = μ + σ * sqrt(2) * erf^-1(2F(x) - 1)

We know that the mean of the tips is $10.70, and the standard deviation is $6.70. Therefore, we can calculate the ICDF of the normal distribution with μ = $10.70 and σ = $6.70.

Then we can find the 90th percentile: x = $10.70 + $6.70 * sqrt(2) * erf^-1(2*0.1 - 1)

Please note that the above calculation required erf^-1(inverse error function) which is not a standard function on most calculators, you may need to use a software/programming language to find it.

As she have 3⅞ pounds of soil, she doesn't have enough soil to fill the flowerpot.

To create a mixed fraction, a suitable fraction and a whole number must be combined. Usually, it denotes a value between 0 and 1. A mixed fraction is one that contains both a whole number and a fraction. One example of a mixed fraction is 1(1/3), where 1 is a whole number and 1/3 is a fraction.

Denise need 4 pounds of soil

By adding the mixed fraction we will know if its enough or not

[tex]$=1\frac{3}{4} + 2 \frac{1}{8}[/tex]

[tex]$=\frac{7}{4} + \frac{17}{8}[/tex]

[tex]$=\frac{14}{8} + \frac{17}{8}[/tex]

[tex]$=\frac{14+17}{8}[/tex]

[tex]= \dfrac{31}{8}[/tex]

[tex]=3 \dfrac{7}{8}[/tex]

Thus, As she have 3⅞ pounds of soil, she doesn't have enough soil to fill the flowerpot.

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The probability of each of the following events are given below:

What is Probability?

Probability is the measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, with 0 representing no chance of the event occurring, and 1 representing a certainty that the event will occur. Probability is widely used in mathematics, statistics, and science to calculate the probability of a given event occurring. It is also used to assess risk and uncertainty in decision-making.

Event A: 0.306 or 30.6%

Event B: 0.44 or 44%.

Event A: The sum is greater than 9.

We have already computed this, the probability of getting a sum greater than 9 is 11/36, which can be simplified as 0.306 or 30.6%

Event B: The sum is not divisible by 2 and not divisible by 5.

To find the probability of this event, we need to find the number of outcomes that have a sum that is not divisible by 2 or 5.

We can calculate this by listing out all the possible outcomes and counting the number that have a sum that is not divisible by 2 or 5: (1,3), (1,4), (1,6), (2,3), (2,5), (3,1), (3,2), (3,4), (3,6), (4,1), (4,3), (4,5), (5,2), (5,4), (6,1), (6,3), (6,4) and (6,6)

There are 16 outcomes that have a sum that is not divisible by 2 or 5, so the probability of getting a sum that is not divisible by 2 or 5 is 16/36, which can be simplified as 0.44 or 44%.

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Answer: 149 cm^3

To find the volume for a cube, the formula is V = a^3, where a = length of one side.

Smaller cube:

a = 3

(3)^3, or 3 x 3 x 3

= 27 cm^3

Larger cube:

a = 5

(5)^3, or 5 x 5 x 5

= 125 cm^3

To find the volume of the entire sculpture, add the volumes of each of the cubes.

27 + 125

= 149 cm^3

The inverse of a function is another function that "undoes" the original function. In other words, the composition of a function and its inverse results in the identity function.

To find the inverse of a function, you can follow these steps:

Replace the function with "y"

Switch the x and y variables

Solve for y (or in this case x)

So in this case, we can find the inverse of 8x^5+7 by replacing y with 8x^5+7, switching the x and y variables, and solving for x:

y = 8x^5+7

x = 8y^5+7

This is not an invertible function because it's not a one-to-one function, it's not a function of x.

Answer:

Hey there! The inverse of 8x^5+7 doesn't exist because it's not a function. Think about it like this, a function is like a machine that takes an input and gives you a unique output. But in this case, the machine isn't working correctly and it doesn't give you a unique output for a given input. So, in simple terms, it doesn't have an inverse.

________________________________________________________

To determine if an equation has an inverse, we need to check if it is a one-to-one function. A one-to-one function is a function in which every unique input corresponds to a unique output. If an equation is one-to-one function, then it has an inverse. If it's not one-to-one function, then it doesn't have an inverse.

To find the inverse of a linear equation, we can follow these steps:

1. Switch the x and y variables

2. Solve for y (or x)

3. Replace y (or x) with f^-1 (x) (or f^-1 (y))

For example, if we have the equation y = 2x+1, we can follow these steps:

1. x = 2y+1

2. x-1 = 2y

3. f^-1(x) = (x-1)/2

So, the inverse of the equation y = 2x+1 is f^-1(x) = (x-1)/2

The ratios that are equivalent to 12:6 are (a) 10 : 5 and (b) 18 : 9

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

Ratio = 12 : 6

Divide both sides of this ratio by 6

So, we have the following representation

Ratio = 2 : 1

Multiply the ratio by 9

Ratio = 18 : 9

Multiply the ratio by 5

Ratio = 10 : 5

Hence, the equivalent ratios are 10:5 and 18:9

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