Semicircles of diameter 2'' are lined up as shown. What is the area, in square inches, of the shaded region in a 1-foot length of this pattern?

Answer:The graph of x = -4 is a vertical line located 4 units to the left of the y-axis.

The domain of x = -4 is the set of all real numbers, since any real number can be plugged into x = -4 and the equation will be true. This is because x = -4 is a vertical line and not a function, it cuts the y-axis at one point, so it doesn't matter what value you put on x it will always be -4.

The range of x = -4 is a single point on the y-axis, y = -4.

Step-by-step explanation:

1/2 as a decimal is 0.5. As a percent, it is 50%. 1/2 can be written as a decimal by dividing the numerator (1) by the denominator (2).

In this case, 1 divided by 2 is 0.5. To convert this decimal to a percent, simply multiply it by 100. 0.5 multiplied by 100 is 50%, so 1/2 as a percent is 50%.

1/2 is 0.5 as a decimal and 50% as a percent.

1/2 is equal to 0.5 when written as a decimal. This means that 1 is divided by 2, resulting in 0.5. To convert this decimal to a percentage, it is necessary to multiply it by 100. When 1/2 is multiplied by 100, it comes out to be 50%, meaning that 1/2 as a percent is 50%. This shows that 1/2 is equal to 0.5 as a decimal and 50% as a percent.

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The number included in the set of integers that when added to -4 gives a sum less than zero are 0, -2 and 3

The question wants us to find the numbers included in the set of integers that when added to -4 gives a sum less than zero.

The options are 3, 7, 9, -2, 4 and 0.

Therefore,

let

the number added = x

Hence,

-4 + x < 0

Base on the options, the numbers that fits into the inequality are as follows:

The numbers are 0, -2 and 3.

Therefore,

-4 + 0 < 0

-4 + -2 < 0

-4 + 3 < 0

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Answer:

  (c)  a reflection across the y-axis followed by a translation 2 units up

Step-by-step explanation:

You want to know transformations that will give the red figure from the blue one.

The red figure is reversed left-to-right with respect to the blue figure, so a reflection across a vertical line is required. The only answer choice that has such a reflection is ...

C. a reflection across the y axis followed by a translation of 2 units up

Answer:

x = 2.5, y = 0.5

Step-by-step explanation:

[tex]10x - 16y = 17\\3x + 3y = 9[/tex]

Isolate for x or y on the equation of choice (Just choose a random one)

[tex]3y = 9 - 3x\\y = 3 - x[/tex]

Sub new equation into the other equation

[tex]10x - 16(3-x) = 17\\10x -48 + 16x = 17\\26x = 65\\x = 2.5[/tex]

Sub x into new equation

[tex]y = 3 - x\\y = 0.5[/tex]

Answer: 15/2

Step-by-step explanation: -5/2 + 1/4W = -5/8

-    1/4W = -5/8 + 5/2

-    1/4W = 15/8

-     W = 15/8 × 4

-      W = 15/2

The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%

Given that,

Mean = 195

Standard deviation = 14

Thus, the probability between 183 and 218 is the ρ value of z when x = 195

Subtracting by the ρ value of z when x = 183

so, x = 218

z = 218-195/14 = 1.64

when x = 183

z = 183-195/14= -0.85

Thus, z value is 1.64 then the probability is 0.94950 and when z value is -0.85 then the probability is 0.21886

Now, 0.94950 - 0.21886 = 0.73064

Therefore, The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%

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hope this helps you understand !!

Answer:

x + 2

Step-by-step explanation:

Ben : x cm

Kieran: (x + 8) cm

Bianca: (x - 2) cm

Mean of their heights = [tex]\frac{Sum of their heights}{Number of people} = \frac{x + (x + 8) + (x - 2)}{3}[/tex]

                                   = [tex]\frac{x + x + 8 + x - 2}{3}[/tex]    (Expand the brackets)

                                   = [tex]\frac{x + x + x + 8 - 2}{3}[/tex]  (Bring all the like terms together)

                      = [tex]\frac{3x + 6}{3}[/tex] (Simplify the two sets of like terms)

                        = [tex]\frac{3(x + 2)}{3}[/tex]  (Extract the common factor '3' in the numerator)

                      = (x + 2) cm  ([tex]\frac{3}{3} = 1[/tex])

Answer:

Let x be the width of the pool. Then the length of the pool is 2x, since it is twice as long as it is wide.

The area of the pool is (2x)(x)=2x^2

The total area of the pool and the walkway is 2x^2+196 square feet.

We can set up the equation using this information:

2x^2 + 22x = 196

Where 22x is the area of the walkway, 22x = 2x * 2 = 4x

2x^2 + 4x = 196

2x^2 + 4x - 196 = 0

Using the quadratic formula to solve the equation above:

x = (-b ± √(b^2 - 4ac))/2a

x = (-4 ± √(4^2 - 42196))/2*2

x = (-4 ± √(16 - 1568))/4

x = (-4 ± √(-1552))/4

Since x is width of the pool, it cannot be a negative value, the x value that is negative must be rejected. Therefore x = (-4 + √1552)/4 = 8

The width of the pool is 8 feet and the length is 2x = 2*8 = 16 feet

Answer:

Nicholas has 5 boys, and Paul has 1 boy

Step-by-step explanation:

We will use 3 different variables, p, j, and n. Along with this, if there is a subscript on a variable, it will be either b or g, meaning boy or girl. If there is no subscript, it means both genders. We will start by translating our sentences into linear equations, giving us:

[tex]p + j + n = 15[/tex]              (1st Equation)

[tex]p_{g} = j_{b} = 3[/tex]              (2nd Equation)

[tex]j = p + 1 (p = 4)[/tex]              (3rd Equation)

[tex]n_{b} = n_{g} +4[/tex]              (4th Equation)

[tex]n_{g} = p_{b}[/tex]              (5th Equation)

Whew! That was a lot.  We know that Paul has 4 children, which means Johnson has 5 children. Which means Nicolas has 6 children. We know that Paul's girl count is 3 (second equation), meaning that 4 - 3 = Paul has 1 boy. Then, we know that Nicholas has:

b = g + 4 and b + g = 6

So, we substitute the first equation into the second equation, giving us:

g + 4 + g = 6

2g = 2

g = 1

So, Nicholas has one girl, meaning he has 5 boys.

So, Nicholas has 5 boys, and Paul has 1 boy.

Hope this helped!

Determining if the method of randomization is either appropriate or not for each given situation includes:

A.           Inappropriate

B.           Appropriate

C.          Appropriate.

Randomization is what?

The technique of randomly assigning study participants to various treatment groups is known as randomization.

Randomization can take the form of selecting names at random to place people in groups or flipping a fair coin to place participants in the experimental or control groups.

In contrast to experiments B and C, the randomization strategy used in experiment A is incorrect.

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Answer:

AB = 6, BC = 6

AB = 4, AC = 4√2

BC = 2√2, AC = 4

(if im not wrong)

Therefore , the solution of the given problem of function comes out to be the function f(x) = x³ + 2x² + 7x - 11  = -1 and g(x) = 3f(x) = -3

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope.

Here,

Given:

we have been provided with -

f(x) = x³ + 2x² + 7x - 11  

so, x = 1

f(x) = 1 +2 +7 -11= -1

g(x) = 3f(x) = -3

Therefore , the solution of the given problem of function comes out to be the function f(x) = x³ + 2x² + 7x - 11  = -1 and g(x) = 3f(x) = -3

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The times more six letter combinations can be formed than four letter combinations will be 26² times.

It should be noted that scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper.

Furthermore, the numbers in the millions place after the decimal required to be represented in a simpler format. As a result, representing a few integers in their expanded form is challenging. As a result, we employ scientific notation.

In this case, the number four letter combination that can be formed with the English alphabet is 26 to the fourth power. The number of six letter combination that can be formed is 26 to the sixth power.

The number of times more six letter combinations can be formed than four letter combinations will be:

= 26^6 / 26^4

= 26^2

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Answer:

26^2

Step-by-step explanation:

Answer:

758.295 meters

Step-by-step explanation:

If for any reason my answer is wrong, feel free to correct me.

As per your question,

The airplanes accelerate uniformly at 2.7 meters per second^2

And they must reach a ground velocity of 64 m/s.

Therefore

S(Displacement) = u(initial velocity) x time + 1/2(acceleration x time^2)

Initial Velocity = 0 m/s(airplane is at rest)
Acceleration is 2.7m/s^2
Time = ?

Acceleration = Final Velocity - Initial Velocity / Time(t)

2.7 m/s^2 = 64 m/s - 0 m/s / t

2.7(t) = 64
t = 64/2.7

t = 23.703703...   rounded to 23.7

S = 0(23.7) + 1/2[2.7 x (23.7)^2]

S = 1/2(2.7 x 561.7)               561.69 is the original answer rounded to 561.7

S = 758.295 meters

Final Answer - An airport would require a runway of minimum length of 758.295 meters to accommodate aircraft of the respective specifications.

2.7 m/s^2 = 64 m/s 0 m/s/t

2.7(t) = 64

t = 64 ÷ 2,7

t = 23.703

or => 23,7

S = 0×(23.7) + 1/2[2,7 × (23,7)²]

S= 1/2(2.7 × 561.7)

S = 758.295 meters

the speed of the plane is 758.295 meters

Answer:

0

Step-by-step explanation:

1/2 = 2/4

1/2-2/4 = 0

A system of 3 linear equations can have 0, 1, or an infinite number of solutions.

A system of linear equations is a group of equations with multiple variables. The number of solutions to the system of equations depends on how many equations and how many variables are in the system. A system of 3 linear equations can have 0, 1, or an infinite number of solutions.

If the number of equations is greater than the number of variables, the system is said to be overdetermined and has no solutions.

If the number of equations is equal to the number of variables, the system is said to be determined and has either one or an infinite number of solutions, depending on if the equations are dependent or independent.

If the number of equations is less than the number of variables, the system is said to be underdetermined and has an infinite number of solutions.

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The number of students who scored between 8181 and 8686 can be calculated using the z-score formula to find standard deviation.

z1 = (8181-7676)/55 = 1.89

z2 = (8686-7676)/55 = 3.04

Using a standard normal table, the area under the curve between these two z-scores is approximately 8.5%. So, we can estimate that about 850,085 students scored between 8181 and 8686. We find the z-score of 8181 and 8686 and calculate the area under the standard normal distribution curve between these z-scores.

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1, while a non-standard normal distribution has a different mean and/or standard deviation. The z-score formula is used to convert a non-standard normal distribution to a standard normal distribution, so that the properties of the standard normal distribution can be applied, such as using a standard normal table to find areas under the curve.

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The range for the function f(x) = 3x² + 18x is option d: [-27 , ∞).

What is the range of a function?

A function's range includes all conceivable values for y. Y = f(x) is the formula to determine a function's range . It is only a function in a relation if each x value has exactly one y value.

The given function is -

f(x) = 3x² + 18x

The set of values of the dependent variable for which a function is defined is a function's range.

For a parabola ax^2+bx+c with vertex (xv,yv) -

If a<0 the range is f(x) ≤ yv.

If a>0 the range is f(x) ≥ yv.

Here a=3, and vertex (xv,yv) = (-3,-27)

So, f(x) ≥ -27.

Therefore, the range is [-27 , ∞).

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The area of the shaded portion is given by the difference between the area of the outer circle and the area of the inner circle.

First, let's find the areas of the circles:

Outer Circle: Area = πr^2 = π (2)^2 = 4π square meters

Inner Circle: Area = πr^2 = π (0.75)^2 = 0.5625π square meters

Area of shaded portion = Area of outer circle - Area of inner circle = 4π - 0.5625π = 3.4375π square meters

So the area of the shaded portion is approximately 10.8 square meters.

The length of the shortest path is 44.69cm.

To find the length of the shortest path, we need to calculate the distance between the two points on the rim of the conical cup where the spider and the fly are located. Since the cone is symmetric, we can find the distance by considering a cross-section of the cone through the center of the cup.

In this cross-section, the spider and the fly are located on a circumference of radius 18 cm (half of the diameter of the cone). The distance between the spider and the fly is one-third of this circumference, or (2pi18 cm)/3 = 12*pi cm.

However, since the cone is 24 cm deep, the shortest path between the spider and the fly is not a straight line, but a curved path along the surface of the cone. To find the length of this path, we need to use the Pythagorean theorem to find the distance between the two points on the surface of the cone.

The height of the cone is 24cm, and the distance between the two points on the circumference is 12pi cm. Using the Pythagorean theorem, we can calculate the length of the shortest path as the square root of (12pi)^2 + 24^2 = 12pi cm + 576 = √(144π^2+ 576)cm=44.69 cm.

So, the length of the shortest path is √(144*π^2+ 576)cm = 44.69cm

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Answer: 43

Step-by-step explanation:

x+x+10 = 96

2x = 86

x = 43

Answer:

the solution is 9/2 = X24

The domain of the given function f(x) = √(x⁴ - 1) include the following: C. {x|x ≤ -1 or x ≥ 1}.

In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined. Additionally, the horizontal extent of a graph represents all domain values (input values) and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Next, we would use an online graphing calculator to plot the graph of the given function f(x) = √(x⁴ - 1). By critically observing the graph of this function shown in the image attached below, we can reasonably and logically deduce the following domain:

Domain = (-∞, 1) U (1, ∞)

By using set builder notation, the domain of this function f(x) = √(x⁴ - 1) can be re-written as follows;

Domain = {x|x ≤ -1 or x ≥ 1}.

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We can draw the conclusion that linear functions can be used to represent each of the ideas. Due to the fact that each proposal's linear function has an initial value, the class now has money in its accounts (b).

A linear function is denoted by the equation y = mx + b, where m is the slope or unit rate between the two variables, x and y, and b is the beginning value or y-intercept.

The initial value is b.

A linear function is a graph with straight lines.

A unit rate exists for all linear functions (b).

Sarah's suggestion can be expressed by a linear function because the graph that represents it is a straight line.

Gene's Proposal's table displays the unit rate as change in y/change in x = 7. As a result, a linear function can be used to express it.

Paul's idea has a linear function as its equation.

This leads us to the conclusion that linear functions can be used to represent each of the ideas.

Due to the fact that each proposal's linear function has an initial value, the class now has money in its accounts (b).

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Correct Question:

The solution of the given equation is x = -3,3. Hence option C is the correct option.

What is a quadratic equation?

A quadratic equation is any equation in algebra that can be rearranged in a standard form where x represents an unknown value and a, b, and c represent known numbers, with a ≠ 0.

The number of solutions of a quadratic equation is 2. The degree of a quadratic equation is also 2.

Given equation is

25x² +64 = 289

Subtract 64 from both sides of the equation:

25x² +64 -64 = 289 -64

25x² = 225

Divide both sides by 25:

25x²/25 = 225/25

x² = 9

Take square root on both sides:

√x² = √9

x = ±3.

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a) Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solution (2,4)

x1=2, x2=4, x1+x2=6

An overdetermined system of linear equations can have infinitely many solutions if the equations are dependent, meaning they are linearly dependent and can be derived from one another by a linear combination. If a system of equations is dependent, it means that the equations are not providing new information.

b) No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of equations below has no solution.

x1=2, x2=4, x1+x2=8

An overdetermined system of linear equations that is not dependent means that the equations are providing new information, but the system has no solutions because there are no free variables, which means there is no way to satisfy all the equations.

d) No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of equations below has no solution.

x1=2, x2=4, x1+x2=24

An overdetermined system of linear equations that is not dependent means that the equations are providing new information, but the system has no solutions because there are no free variables, which means there is no way to satisfy all the equations.

c) is not a valid option as it contains a mix of concepts of dependent and independent systems and also the system of equations is inconsistent.

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Answer:

I hope my answer is helpful!

"안녕하세요" is a formal and polite way of saying "hello" in Korean. It is commonly used as a greeting, both when meeting someone for the first time and when meeting someone again after a period of time. The literal translation of 안녕하세요 is "Are you at peace?"

Answer:

5:4

Step-by-step explanation:

girls = 4

boys = 5

ratio = boys:girls = 5:4

HOPE THIS HELPED