a piece of wire 10m long is cut into 2 pieces. one piece is bent into a square and the other into a circle. how much of the wire should be used for the square if you want to minimize the total enclosed area? please give an exact simplified answer.

If the random variable X is distributed normally with a mean of 0 and a standard deviation of 1, the probability P(x = 0) =.50 is not correct.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means.

The probability of all the events in a sample space adds up to 1.

Thus, If the random variable X is distributed normally with a mean of 0 and a standard deviation of 1, the probability P(x = 0) =.50 is not correct.

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Answer:

Step-by-step explanation:

true true false

Answer:

[tex]\boxed{\displaystyle f^{-1}(x) =\left(\dfrac{x-2}{4}\right)^5 + 1\\}[/tex]

This is the last choice on the screenshot you provided

Step-by-step explanation:

Use y to represent f(x)

[tex]y=4\sqrt[5]{x-1}+2[/tex]

Replace x with y and y with x:

[tex]x=4\sqrt[5]{y-1}+2[/tex]

Solve for y in terms of x and that will be the inverse of f(x)

Answer: Last choice on the screen, namely

[tex]\boxed{\displaystyle f^{-1}(x) =\left(\dfrac{x-2}{4}\right)^5 + 1\\}[/tex]

Answer:

[tex]y=-\frac{2}{3}x+4[/tex]

Step-by-step explanation:

[tex]y=\frac{4-0}{0-6}=-\frac{2}{3} \\ \\ b=4 \implies y=-\frac{2}{3}x+4[/tex]

The polynomial x⁵ - 4x³ + x² - 4 will have a remainder of -8 when divided by x² - x + 1 and the result can be written in the form (x³ + x² - 4x + 4) - 8/(x² - x + 1).

Using the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder

We shall divide the polynomial x⁵ - 4x³ + x² - 4 by x² - x + 1 as follows;

x⁵ divided by x² equals x³

x² - x + 1 multiplied by x³ equals x⁵ - x⁴ + x³

subtract x⁵ - x⁴ + x³ from x⁵ - 4x³ + x² - 4 will result to x⁴ - 5x³ + x² - 4

x⁴ divided by x² equals x²

x² - x + 1 multiplied by x² equals x⁴ - x³ + x²

subtract x⁴ - x³ + x² from x⁴ - 5x³ + x² - 4 will result to -4x³ - 4

-4x³ divided by x² equals -4x

x² - x + 1 multiplied by -4x equals -4x³ + 4x² - 4x

subtract 4x³ + 4x² - 4x from -4x³ - 4 will result to 4x² - 4x - 4

4x² divided by x² equals 4

x² - x + 1 multiplied by 4 equals 4x² - 4x - 4

subtract 4x² - 4x - 4 from 4x² - 4x - 4 will result to a remainder of -8.

Therefore, the polynomial x⁵ - 4x³ + x² - 4 divided by x² - x + 1 gives a quotient x³ + x² - 4x + 4 and a remainder of -8 and can be written as (x³ + x² - 4x + 4) - 8/(x² - x + 1).

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Answer: number 1: 0.1111 and number 2: 1.0909

Step-by-step explanation: I hope I did this right

  The ant's entire distance travelled along its semicircular journey is its total distance travelled overall. The ant is travelling around a circle with radius R, thus the distance it has travelled is equal to half of the circle's circumference, πR.

The change in the ant's position is represented by a vector quantity called the displacement of the ant. The ant in this scenario begins at one end of the semi-circular path and moves 2R away from the beginning point to reach the other end. The direction of the displacement vector is from the starting point to the ending point, and the displacement's magnitude is equal to the 2R distance between the two points.

    So, the option c is most suitable option.

Therefore, πR and 2R are the ant's displacement and the distance travelled, respectively.

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The sequence of numbers for the expression -n² - 2n + 3 is

0, -5, -12, -21, and -32.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

-n² - 2n + 3

The sequence of numbers for n = 1, 2, 3, 4, 5 are:

n = 1,

-1 - 2 + 3

= -3 + 3

= 0

n = 2,

-4 - 4 + 3

= -8 + 3

= -5

n = 3,

-9 - 6 + 3

= -15 + 3

= -12

n = 4,

-4² - 2 x 4 + 3

= -16 - 8 + 3

= -21

n = 5,

-25 - 10 + 3

= -35 + 3

= -32

Thus,

The sequence of numbers is 0, -5, -12, -21, and -32.

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Yes, it is possible for a data set to have no mode.

A mode is the most common value in a data set, so if there are no observations that occur more than once, the data set would have no mode. For example, a data set of the numbers {1, 2, 3, 4, 5} would have no mode because none of the numbers appear more than once.

Additionally, a dataset can also have multiple modes, or a bimodal distribution, which means that there are two or more observations that occur with the same highest frequency. A dataset can have a multimodal distribution as well if it has more than two modes.

In summary, a dataset can have no mode if no observations occur more than once, or have multiple/multimodal modes if more than one observations occur with the same highest frequency.

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0.5x + 6 = 4x - 1

3.5x = 7

x = 2

Only one solution exists for the given equation.

Answer:

one

Step-by-step explanation

For a polynomial function, the number of solutions, or zeros, is generally equivalent to the highest degree. For example, a cubic function (e.g. [tex]x^3+2x^2[/tex]) has 3 real zeros (x=-2, x=0, and x=0) and a quadratic (e.g. [tex]x^2-1[/tex]) has 2 real zeros (x=-1 and x=1).

For your problem, [tex]\frac{1}{2} (x+12)=4x-1[/tex], the highest degree is 1 since this is a linear function. To prove there is only one solution, let's bring all the terms to one side, simplify, and solve for x.

There only one solution to the equation as shown above and as can be seen in step 4, the x is only to the first degree ([tex]x=x^1[/tex]) which indicates that there is only one solution, 2.

Answer:

58.4%

Step-by-step explanation:

Answer:

The number that gives the same result if it is multiplied by 999/998 or if any number is added to it is zero (0).

The property of a number being unchanged after being multiplied by a fraction and a constant is called an "Identity element". The identity element for multiplication is 1 and for addition is 0.

When any number is multiplied by 1, it stays the same. So, if we multiply any number by 999/998, which is equivalent to multiplying by 1, it stays the same.

Similarly, when any number is added to zero, it stays the same. So, if we add any number to 0, it stays the same.

Therefore, the only number that gives the same result if it is multiplied by 999/998 or if any number is added to it is zero (0).

Answer:

Step-by-step explanation:

The power of 10 is the exponent of places we move the decimal point to get the first factor. For any number greater than 1, the power of 10 in scientific notation will be positive.

First Non-zero Power of 10

Example: Let’s look at the mass of Earth in kilograms.

What power? 9

Numbers can also be converted from scientific notation to standard notation.

Look at the number 6.51 × 108 . The power of 10 denotes the number of places the decimal point has to move. The power of 10 in this number is positive, so we move the decimal point to the right 8 places.

The number 6.51 × 108 written in standard notation is 651000000.

Answer:

y = -4x

Step-by-step explanation:

When equations are in the form

y = mx  the slope m (is y/x)

The expected value of the number of marbles Zuri removes from the bag is the sum of the number of red marbles plus the number of blue marbles.

The expected value of the number of marbles Zuri removes from the bag is the sum of the number of red and blue marbles. This is because the expected value of an event is the sum of the probability of each outcome multiplied by the associated outcome. Since Zuri is randomly removing marbles from the bag, one at a time and without replacement, the probability of each outcome (red or blue) is equal. Therefore, the expected value of the number of marbles Zuri removes from the bag is the sum of the number of red marbles plus the number of blue marbles. This is because each marble has an equal chance of being removed and, therefore, each marble has the same expected value.

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Answer:

We can use the following steps to determine the different amounts of money that can be made from a collection of coins that consists of two pennies, one nickel, and one dime:

Step 1: List out all the different combinations of coins that can be used to make the different amounts of money.

Two pennies

One penny and one nickel

One penny and one dime

Two pennies and one nickel

Two pennies and one dime

One nickel and one dime

Two pennies, one nickel, and one dime

Step 2: Calculate the value of each combination of coins.

Two pennies = $0.02

One penny and one nickel = $0.06

One penny and one dime = $0.11

Two pennies and one nickel = $0.07

Two pennies and one dime = $0.12

One nickel and one dime = $0.15

Two pennies, one nickel, and one dime = $0.17

Step 3: Write down the total amount of money that can be made from each combination.

Final Answer: There are 7 different amounts of money that can be made from a collection of coins that consists of two pennies, one nickel, and one dime, they are $0.02, $0.06, $0.11, $0.07, $0.12, $0.15, and $0.17

6 points were scored in the 11th game.

Mean is the arithmetic average of a set of given numbers. Therefore the mean in math is often referred to as simply the average.

The mean is the total number of points scored divided by the number of games.

So if the mean is 17 points per game for the first 10 games, the total number of points scored in the first 10 games is 17 * 10 = 170.

Similarly,

if the mean is 16 points per game after the 11th game, the total number of points scored in the first 11 games is 16 * 11 = 176.

To find the number of points scored in the 11th game

we can subtract the total number of points scored in the first 10 games from the total number of points scored in the first 11 games:

176 - 170 = 6

Therefore, 6 points were scored in the 11th game.

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Answer:

1. Write the number as the numerator of the fraction.

2. Write 1 as the denominator of the fraction.

Step-by-step explanation:

Example-

To turn the number 3 into a fraction, write 3 as the numerator and 1 as the denominator. The resulting fraction is 3/1.

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Check the picture below.

The area of the shaded portion of the figure is 272 units squared.

The figure above is a triangle inside a trapezium. The area of the shaded portion can be found when we subtract the area of the triangle from the area of the trapezium.

Therefore,

area of the shaded portion = area of the trapezium - area of the triangle

area of the triangle = 1 / 2 bh

where

Therefore,

area of the triangle = 1 / 2 × 18 × 16

area of the triangle = 288 / 2

area of the triangle = 144 units²

area of the trapezium = 1 / 2 (a + b)h

where

Therefore,

area of the trapezium = 1 / 2 (18 + 34)16

area of the trapezium = 1 / 2 (52)16

area of the trapezium =  832 / 2

area of the trapezium = 416 unit²

Therefore,

area of the shaded portion = 416 - 144

area of the shaded portion = 272 units²

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First of all, we need to know what the units are in this problem.

We can see that there is yards, inches, and feet.

(Keep in mind that yd = yard, ft = feet, and in = inches)

1yd = 3ft

1ft = 12in

Let's figure out how many inches are in a yard.

If we know that 3 feet are in every yard, and 12 inches are in every foot, we can make an equation that looks like this:

(1yd × 3ft) × 12 = 36

This means that there are 36 inches in every foot.

Now that we know how many inches are in a yard, lets figure out how many inches are in 10 yards.

36 × 10 = 360

There are 360 inches in 10 yards.

Now, let's figure out how much 360 inches exceeds 192 inches.

360 - 192 = 168

To convert this to feet, we need to use an equation that looks like this:

168 ÷ 12 = 14

Therefore, the amount of feet that the length of the room exceeds the width is 14 feet.

To find the domain and range of a system of inequalities, you need to solve the system of inequalities, plot the solution, determine inequality sign for solution, shade area of solution, then the x-values of the area represent domain and y values represent range.

Solve the system of inequalities for x and y in terms of each other.

Plot the solutions on a coordinate plane. Each solution will be a boundary line for the solution set.

Determine the inequality signs for each solution. Solutions with < or > signs will be represented as a dashed line, while solutions with ≤ or ≥ signs will be represented as a solid line.

Shade the portion of the coordinate plane that satisfies all of the inequalities.

The shaded area represents the solution set for the system of inequalities.

The domain is the set of all x-values that are included in the solution set and the range is the set of all y-values that are included in the solution set.

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The supplied statement states that the function f(maverage )'s rate of change is 0.78 cm, representing the fish's original length.

A function in mathematics is an expression, rule, or law that determines the link between two variables, one of which is an independent variable (the dependent variable). Functions may be present everywhere in mathematics, and they are essential for building physical connections in the sciences.

The fish's original length, which is represented by the graph's y-intercept, is 5 cm.

The function f(maverage )'s rate of change at m = 3 to m = 7

m = 3 => f(3) = 5(1.08) = 5.4 cm

m = 7 => f(7) = 5(1.08)⁷ = 8.55 cm

Change in 9 - 1 = 8 months = 8.55 - 5.4 = 3.15 cm

The function's average variation at m = 3 through m = 7 is given.

= (3.15/4)

= 0.78 cm per month

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We can create a total number of 10 prime numbers from the set {1, 3, 6, 7}.

Given that,

The number is either 1-digit or 2-digit.

In the case of 1-digit, the only 1-digit primes are 3 and 7, for a total of 2 primes.

In the case of 2-digit, We have the following combinations of numbers: 13, 16, 17, 36, 37, 67, 76, 73, 63, 71, 61, 31. Out of these 12 numbers, it is easier to count the composites: 16, 36, 76, and 63 for a total of 4 composites, which we subtract from the original 12 numbers to yield 12-4=8 prime numbers.

Thus, We can create a total number of 10 prime numbers from the set {1, 3, 6, 7}.

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For given function f(x) the y in the graph are f(2) = 4,f(0) = 3 ,f(-6) = -6 and f(4) = 5

A function is described as a relationship between a set of inputs, each of which has a single output. The simplest definition of a function is an association between inputs where each input is connected to a single, unique output. There is a codomain or range for each function. A function is frequently referred to as f(x), where x is the input.

Here,

In the given graph

when x = 2

y = 4

and x = 0

y = 3

Put it in slope formula

=> m =y2 - y1 / x2 -x1

=>  m =1/2

m = 1/2

Now we can just put them into slope formula

y - y₁ = m(x - x₁)

y - 4 = 1/2(x - 2)

y = 1/2(x) -1 + 4

y = 1/2(x) + 3

Now we can just put them into slope formula

y - y₁ = m(x - x₁)

y - 3 = 1/2(x - 0)

y = 1/2(x)  + 3

Thus, the function for given f(x) is solved

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Answer:

  -4y²

Step-by-step explanation:

You want to simplify the expression -√(16y⁴), given that y < 0.

The square root can be simplified by removing squares from under the radical.

  [tex]-\sqrt{16y^4}=-\sqrt{(4y^2)^2}=\boxed{-4y^2}[/tex]

The sign of y is irrelevant.

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The above statement suggests that perhaps the curve's approximate length is 2.

Curve, An abstract phrase used only to describe the trajectory of a linearly stretching point in mathematics (see continuity). Usually, an equation will create such a route. The term may also be used to describe a linear model or a collection of connected line segments. The curve is referred to as a route, or a plot line (or just arc). If a curve is the continuous injective picture of either an interval or indeed a circle, it is considered simple.

Considering function is,

[tex]y=\sqrt{x-x^2}+\sin ^{-1} \sqrt{x}[/tex]

To determine the curve's actual length

First ,  Parametrise  the Curve  by x = sin²u

[tex]\begin{aligned}& y=\sqrt{\sin ^2 u-\sin ^4 u}+\sin ^{-1} \sqrt{\sin ^2 u} \\& y=\sin u \sqrt{1-\sin ^2 u}+\sin ^{-1} \sin u\end{aligned}[/tex]

y = sinucosu + u

[tex]\begin{aligned}& y=\frac{1}{2} \times 2 \sin u \cos u+u \\& y=\frac{\sin 2 u}{2}+u \\& \frac{\mathrm{d} y}{\mathrm{~d} u}=\frac{\mathrm{d}}{\mathrm{d} u}\left[\frac{\sin 2 u}{2}+u\right] \\& \frac{\mathrm{d} y}{\mathrm{~d} u}=\left[\frac{2 \cos 2 u}{2}+1\right]\end{aligned}[/tex]

[tex]\frac{\mathrm{d} y}{\mathrm{~d} u}=[\cos 2 u+1][/tex]

and, x = sin²u

[tex]\begin{aligned}& \frac{\mathrm{d} x}{\mathrm{~d} u}=\frac{\mathrm{d}}{\mathrm{d} u}\left[\sin ^2 u\right] \\& \frac{\mathrm{d} x}{\mathrm{~d} u}=[2 \sin u \cos u] \\& \frac{\mathrm{d} x}{\mathrm{~d} u}=[\sin 2 u] \\& \left(\frac{\mathrm{d} s}{\mathrm{~d} u}\right)^2=\left(\frac{\mathrm{d} x}{\mathrm{~d} u}\right)^2+\left(\frac{\mathrm{d} y}{\mathrm{~d} u}\right)^2 \\& \left(\frac{\mathrm{d} s}{\mathrm{~d} u}\right)^2=(\sin 2 u)^2+(1+\cos 2 u)^2\end{aligned}[/tex]

[tex]\begin{aligned}\left(\frac{\mathrm{d} s}{\mathrm{~d} u}\right)^2 & =\left[\sin ^2 2 u+1+\cos ^2 2 u+2 \cos 2 u\right] \\\left(\frac{\mathrm{d} s}{\mathrm{~d} u}\right)^2 & =[1+1+2 \cos 2 u] \\\left(\frac{\mathrm{d} s}{\mathrm{~d} u}\right)^2 & =[2+2 \cos 2 u] \\\left(\frac{\mathrm{d} s}{\mathrm{~d} u}\right)^2 & =4 \cos ^2 u \\\left(\frac{\mathrm{d} s}{\mathrm{~d} u}\right)^2 & =2 \cos u\end{aligned}[/tex]

Currently, the curve's exact length is,

[tex]\begin{aligned}& =\int_0^{\Pi / 2} 2 \cos u d u \\& =2 \int_0^{\Pi / 2} \cos u d u \\& =2[\sin u]_0^{\Pi / 2} \\& =2\left[\sin \frac{\Pi}{2}-\sin 0\right]\end{aligned}[/tex]

= 2

As a result, the curve's exact length is 2

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Yes, it makes sense that the number of cats falling from 5th floor would be greater since the terminal velocity of the cat would be greater at higher altitudes.

The pace at which an object's location changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.

A distance measurement between a reference datum and a point or object, typically in the vertical or "up" direction, is known as altitude, height, or depth.

The terminal velocity of the cat would be greater at higher altitudes; hence cats have higher risk of falling from heights.

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Listing of the angles and the sides in the order of smallest to largest is given by :

Side opposite to obtuse angle > Side opposite to acute angle and

side opposite to right angle > side opposite to acute angle.

As given in the question,

In the given triangle,

Ordering of the angles and sides from smallest to largest.

As per the property of the triangle:

Side opposite to the greatest angle is the largest side of the given triangle.

If the given triangle is obtuse angle triangle,

Then other two angles are acute.

Compare all the angles and sides arrange in ascending order.

Side opposite to obtuse angle  > Side opposite to acute angle

In the right angled triangle,

Other two angles are acute.

Same compare and write in ascending order.

side opposite to right angle > side opposite to acute angle

Therefore, the sides and angles can be written in smallest to largest order by comparison and is given by:

Side opposite to obtuse angle  > Side opposite to acute angle and

side opposite to right angle > side opposite to acute angle.

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Answer:

57 grey plates

Step-by-step explanation:

304 = 3 : 8 : 5

304 = 16x

[tex] \frac{ \\ 304}{16} = \frac{16x}{16} [/tex]

x = 19

by solving systematically for the grey plate

3 × 19 = 57 grey plates.

Additional solvings.

by solving systematically for the white plates

8 × 19 = 152 white plates

by solving systematically for the black plates

5 × 19 = 95 black plates

Total plates

57 + 152 + 95 = 304

I hope this helped