Helena sketches a circular backyard skating pond that fits into a square
section of her yard. In her sketch, what is the area of the shaded region?
Factor out the GCF. Explain.

The interval notation for the inequality statement "5 less than m is at most 70" is (-∞, 75].

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The statement given is - 5 less than m is at most 70.

The given sentence can be translated into a mathematical inequality as -

m - 5 ≤ 70

To solve for m, we can add 5 to both sides of the inequality -

m - 5 + 5 ≤ 70 + 5

m ≤ 75

Therefore, m is less than or equal to 75.

In interval notation, we can represent this solution as -

(-∞, 75]

Therefore, the interval value is (-∞, 75].

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We can write the number in scientific nοtatiοn as: $1.5489*107 = 1.5489 * 10 pοwer 7$ This is the standard nοtatiοn fοr the given number.

Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants.

In scientific nοtatiοn, a number is expressed as the prοduct οf a decimal number between 1 and 10 (called the cοefficient) and a pοwer οf 10 (called the expοnent). The expοnent indicates hοw many places the decimal pοint needs tο be mοved tο οbtain the οriginal number.

In the given number, $1.5489*107$, the cοefficient is 1.5489, and the expοnent is 7, which means the decimal pοint needs tο be mοved 7 places tο the right tο οbtain the οriginal number.

Therefοre , we can write the number in scientific nοtatiοn as: $1.5489*107 = 1.5489 * 10 pοwer 7$ This is the standard nοtatiοn fοr the given number.

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Regan invested the money for 8 years at simple interest to earn $2000.

Simple interest is calculated on the loan amount or principle amount, whereas compound interest is calculated using both the principal amount and the interest that has accrued over the course of a prior period or particular time. Simple interest is based on the principal amount, which is the main distinction between it and compound interest. Contrarily, compound interest is calculated using the principle sum and interest that has been compounded over the course of a period.

The simple interest is given as:

SI = Prt

where I is the interest earned.

P is the principal, = 500.

is the interest rate = 5% = 0.05.

t is the time (in years).

Substituting the values:

2000 = 500 * 0.05 * t

t = 8 years

Hence, Regan invested the money for 8 years at simple interest to earn $2000.

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Answer:

The number of additional streetlights installed every week is 2, and this will continue for 52 weeks. Therefore, the total number of streetlights added during this period will be:

2 streetlights/week x 52 weeks = 104 streetlights

If the city currently has 138 streetlights, then after 30 weeks, the total number of streetlights will be:

138 streetlights + 2 streetlights/week x 30 weeks = 198 streetlights

Therefore, the city will have 198 streetlights at the end of 30 weeks.

Step-by-step explanation:

1. The problem states that the city currently has 138 streetlights.

2. The city council has decided to install 2 additional streetlights at the end of each week for the next 52 weeks. This means that every week, the city will add 2 streetlights to its total.

3. To find out how many streetlights will be added in total over the 52-week period, we can multiply the number of additional streetlights per week (2) by the number of weeks (52):

2 streetlights/week x 52 weeks = 104 streetlights

Therefore, over the 52-week period, the city will add 104 streetlights.

4. To find out how many streetlights the city will have at the end of 30 weeks, we need to calculate how many additional streetlights will be added during this time period. Since the city is adding 2 streetlights per week, we can multiply 2 by the number of weeks (30):

2 streetlights/week x 30 weeks = 60 streetlights

This means that over the course of 30 weeks, the city will add 60 streetlights.

5. To find out the total number of streetlights at the end of 30 weeks, we need to add the current number of streetlights to the number of streetlights added during the 30-week period. Therefore, we can add 138 (the current number of streetlights) and 60 (the number of streetlights added during the 30-week period):

138 streetlights + 60 streetlights = 198 streetlights

Therefore, the city will have 198 streetlights at the end of 30 weeks.

Chris can obtain a random sample of 50 residents by surveying the first 25 women and 25 men at a grocery store, surveying every 10th woman and every 10th man from a list of people living in the town, surveying one person from every 10th home in the town, or surveying the first 50 people he saw at the airport as he got off the plane.

Random sampling is an important method used to obtain a representative sample of the population of interest. Random sampling involves selecting a sample of elements from a population in such a way that each element has an equal probability of being selected. This ensures that the sample is not biased in any way and that it is representative of the population.In order to obtain a random sample, Chris could use a variety of methods. He could survey the first 25 women and 25 men he met at a grocery store, survey every 10th woman and every 10th man from a list of people living in the town, survey one person from every 10th home in the town, or survey the first 50 people he saw at the airport as he got off the plane.Each of these methods would result in a sample of 50 people that is randomly selected from the population of 500 residents. This would ensure that the sample is representative of the population and that the results of the survey are not biased in any way. Furthermore, the sample size of 50 is large enough to be considered representative of the population of 500.

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The volume generated by rotating the region bounded by the curves [tex]$x = \sqrt{y}$[/tex], [tex]$x = 0$[/tex], and [tex]$y = 4$[/tex] about the x-axis using the method of cylindrical shells is [tex]$4\pi$[/tex] cubic units.

The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

To find the volume generated by rotating the region bounded by the curves [tex]$x = \sqrt{y}$[/tex], [tex]$x = 0$[/tex], and [tex]$y = 4$[/tex] about the x-axis using the method of cylindrical shells, we need to follow these steps:

Sketch the region and the axis of rotation. The region bounded by the curves [tex]$x = \sqrt{y}$[/tex], [tex]$x = 0$[/tex], and [tex]$y = 4$[/tex] is a quarter-circle with radius 2 centered at the origin. The axis of rotation is the x-axis.

Choose a vertical strip with width $\Delta x$ that runs parallel to the y-axis and intersects the region. The height of this strip is given by the equation $y = 4 - x^2$.

Imagine rotating this strip around the x-axis to form a cylindrical shell with thickness [tex]$\Delta x$[/tex], height [tex]$4 - x^2$[/tex], and radius [tex]$x$[/tex].

The volume of this cylindrical shell is given by the formula [tex]$V = 2\pi x(4-x^2)\Delta x$[/tex].

To find the total volume of the solid, we need to add up the volumes of all the cylindrical shells. This can be done by taking the limit as the width of the strips $\Delta x$ approaches zero and summing up the volumes of the resulting shells. This gives us the integral:

[tex]$V = \int_{0}^{2} 2\pi x(4-x^2) dx$[/tex]

We can simplify this integral by expanding the expression inside the parentheses, which gives us:

[tex]$V = \int_{0}^{2} 8\pi x - 2\pi x^3 dx$[/tex]

We can then integrate each term separately to get:

[tex]$V = [4\pi x^2 - \frac{1}{2}\pi x^4]_{0}^{2}$[/tex]

[tex]$V = (4\pi \cdot 2^2 - \frac{1}{2}\pi \cdot 2^4) - (4\pi \cdot 0^2 - \frac{1}{2}\pi \cdot 0^4)$[/tex]

[tex]$V = 8\pi - 4\pi = 4\pi$[/tex]

Therefore, the volume generated by rotating the region bounded by the curves [tex]$x = \sqrt{y}$[/tex], [tex]$x = 0$[/tex], and [tex]$y = 4$[/tex] about the x-axis using the method of cylindrical shells is [tex]$4\pi$[/tex] cubic units.

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The system of equations modeling the number of imports and the number of exports is given as follows:

The solution f(x) = g(x) represents the month at which the number of imports and the number of exports was the same.

The system of equations is modeled by linear functions in slope-intercept form, as follows:

y = mx + b.

In which:

Hence the equations are given as follows:

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The inequalities are factorized to;

1. x > 5 and x > -1          

x > 2 and x > -6

2. x < 2

x < -4 and x < 2

3. x > 7

x> 1 and x> 3

From the information given, we have the inequalities;

(x - 5)(x + 1)> 0

expand the bracket, we get;

x² + x - 5x - 5> 0

x(x + 1) - 5(x + 1) > 0

x > 5 and x > -1

2. x-2/x + 3 < 0

cross multiply the values

x - 2< 0

make 'x' the subject

x < 2

3. x -7/x + 4 > 0

cross multiply the values

x - 7> 0

make 'x' the subject

x > 7

x² + 4x - 12 > 0

x² + 6x - 2x - 12> 0

Factorize

x(x + 6) - 2(x + 6)> 0

x > 2 and x > -6

x² - 2x - 8< 0

x² -2x + 4x - 8 < 0

Factorize

x(x - 2) + 4(x -2 )< 0

x < -4 and x < 2

x² - 4x + 3 > 0

x² - 3x - x + 3> 0

factorize

x(x - 3) - 1(x - 3)> 0

x> 1 and x> 3

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Therefore, the number of animals at the start of year 3 is approximately 408.04.

An equation is a mathematical statement that shows the equality of two expressions, usually with an equal sign "=" in between them. An equation can contain variables, constants, and operators. The variables are represented by letters and can take on different values, while constants are fixed values that do not change. Operators include mathematical symbols like plus, minus, multiplication, and division, as well as exponents and logarithms.

Here,

We are given that the population at the start of year 1 (P1) is 400. Using the recurrence relation Pt + 1 = 1.01Pt, we can find the population at the start of year 2 (P2) and year 3 (P3) as follows:

P2 = 1.01 * P1 = 1.01 * 400 = 404

P3 = 1.01 * P2 = 1.01 * 404 = 408.04

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Answer: The interest rate per quarter is 5%/4 = 1.25%.

At the end of the first quarter, the balance is:

$1000 + $1000(1.25%) = $1000 + $12.50 = $1012.50

At the end of the second quarter, the balance is:

$1012.50 + $1012.50(1.25%) = $1012.50 + $12.66 = $1025.16

At the end of the third quarter, the balance is:

$1025.16 + $1025.16(1.25%) = $1025.16 + $12.82 = $1037.98

At the end of the fourth quarter, the balance is:

$1037.98 + $1037.98(1.25%) = $1037.98 + $13.00 = $1050.98

Therefore, the year-end balance is $1050.98 (rounded to the nearest penny).

Step-by-step explanation:

1 )Use the algorithm method.

            5 0

×         2 1 2

          1

          100

         500

    1

     10000

     10600

2) Therefore,50×212=10600

              10600

Answer:

To find the lowest form of 28 upon 36, we need to simplify or reduce the fraction to its lowest terms. This can be done by finding the greatest common factor (GCF) of the numerator (28) and the denominator (36) and dividing both by it.

First, we can find the prime factors of 28 and 36:

28 = 2 × 2 × 7

36 = 2 × 2 × 3 × 3

Next, we can identify the common factors, which are 2 and 2.

To find the greatest common factor, we need to multiply the common factors together. In this case, 2 × 2 = 4, so the greatest common factor is 4.

Now we can divide both the numerator and the denominator by the GCF:

28 ÷ 4 = 7

36 ÷ 4 = 9

Therefore, the lowest form of 28 upon 36 is 7/9.

Step-by-step explanation:

Answer:

give full question please its not full

Answer:

95% of that number is 361

Step-by-step explanation:

Let's start by finding the actual value of the number.

If 80% of a number is 304, we can set up the equation:

0.8x = 304

To solve for x, we can divide both sides by 0.8:

x = 380

So the number is 380.

Now we can use the second piece of information to find 15% of the number:

0.15(380) = 57

This confirms that our value for x is correct.

Finally, we can use this information to find 95% of the number:

0.95(380) = 361

Therefore, 95% of the number is 361.

Answer: 0

Step-by-step explanation:

1. Bring the Variables to one side and the constants to the other (3n + 2n + 3n = 7 - 7)

2. Solve ( 8n = 0, n = 0/8, n = 0)

The mapping of the functions h(x) = |x|/2, f(x) = 2x + 8, and f(x) = x² - 5x + 2 is defined at;

1). -2, f(-2) = 1

2). 6, f(6) = 20

3). 2, f(2) = -4

A function is a rule that defines a relationship between one variable. It is the mapping whose codomain is the set of real numbers

For x = -2;

h(-2) = |-2|/2

h(x) = 2/2 {absolute value of -2 is 2 units}

h(x) = 1

for x = 6;

f(6) = 2(6) + 8

f(6) = 12 + 8

f(6) = 20

for x = 2;

f(2) = (2)² - 5(2) + 2

f(2) = 4 - 10 + 2

f(2) = -4

Therefore, the mapping of the functions h(x) = |x|/2, f(x) = 2x + 8, and f(x) = x² - 5x + 2 is defined at;

1). -2, f(-2) = 1

2). 6, f(6) = 20

3). 2, f(2) = -4

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Option B. g(x)=(x-2)²is the equation of blue graph.

A graph is a visual representation or diagram that displays facts or values in an organized manner in mathematics.

The red graph is represented by the function:

f(x)=x²

Also, we need the formula for the blue graph.

We can see that the blue graph is just the red graph with the horizontal axis moved 2 units to the right.

An example of a horizontal transition is:

f(x-h) where h is the quantity we shift (to the right).

h = 2 since we moved two units to the right.

Our new role will thus be:

g(x)=f(x-2)=(x-2)²

Therefore:

g(x)=(x-2)²

Our response is B.

Notes:

A denotes a downward vertical movement of two units.

C (assuming it is x²) denotes a two-unit vertical displacement upward.

And D (if you let h = -2, then f(x - (-2)) = f(x + 2) = (x + 2)²) is a horizontal shift of two units to the left.

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the complete question is:

The graphs below have the same shape. What is the equation of the blue

graph?

f(x) = x2

g(x) = ?

9(x) =

O A. g(x) = x² - 2

B. g(x) = (x - 2)2

c. g(x) = x + 2

D. Q(x) = (x + 2)2

Image is attached below;

Answer:

3(5x+7)-6 (4-2x)

15x+21-24+12x = 27x-3

or

15x+21-6+4-2x = 13x+19

Answer:

a

Step-by-step explanation:

16÷4 is 4 and 12÷4 is 3. I matched up the angles.

After calc, the lenght of AC segment is 3 cm. Alternative A

The similarity of triangles property has a way of calculating how much an unknown segment of the triangle is worth through measures of available equivalent segments of the two triangles and matching angles.

[tex]\begin{array}{l}\raisebox{8pt}{$\sf \dfrac{AC}{BC}=\dfrac{DF}{EF}$}\\\raisebox{8pt}{$\sf \dfrac{AC}{4}=\dfrac{\red{\diagup\!\!\!\!\!\!12}^{\div4}}{\red{\diagup\!\!\!\!\!\!16}^{\div4}}$}\\\raisebox{8pt}{$\sf \dfrac{AC}{\red{\diagup\!\!\!\!4}}=\dfrac{3}{\red{\diagup\!\!\!\!4}}$}\\\bf\therefore AC=3\end{array}[/tex]

Found the length of segment AC, which is 3cm

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If you have any question about this solution, you can ask me in the comments :)

Answer:

Step-by-step explanation:

Find the area of the outer trapezoid and then subtract the area of the inner trapezoid.

[tex]A=\frac{1}{2} (a+b)h[/tex]

[tex]A_o=\frac{1}{2} (6+2)6=24[/tex]

[tex]A_i=\frac{1}{2} (4+2)3=9[/tex]

Total area = 24 - 9 =15 square units

The dοtted line is the line y=13x3, and the shaded area is abοve it.

As is well knοwn, the equatiοn fοr a straight line is y = mx + c. Where 'c' is the y-axis intercept and 'm' is the slοpe οn the y-axis. The fοrmula fοr a hοrizοntal line is y = 3.

In οrder tο graph the inequality y≥13x−3, we can first plοt the line y=13x3

(which has a slοpe οf 13 and a y-intercept οf -3) as a dοtted line.

Since the inequality is y≥13x−3, we must shade the area abοve the line.

The dοtted line is the line y=13x3, and the shaded area is abοve it.

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Answer: B

V=957.7 cubic inches

Step-by-step explanation:

V=Hxpixr^2

V=12.2x3.14x5^2           r=5 because it is half of the diamter, which is 10.

V=12.2x3.14x25

V=957.7 cubic inches

Answer:

X= 25

Step-by-step explanation:

The answer is shown above!

Hypotenuse equals opposite/tan(45°) = 300/1 = 300 feet. Boat A is therefore 300 feet horizontally away from the lighthouse.

The numerical measurement of distance is the separation between two objects or points. Typically, it is expressed in terms of metres, kilometres, miles, or feet. Distances can be calculated either along a simple path (the Euclidean distance) or along a more complicated one (such as a curved surface or a circuitous route). Distance is a crucial notion that is used to define the separation between things, the length of a route or path, and the displacement of an object through time in many disciplines, including physics, mathematics, geography, and engineering.

given

We may utilise trigonometry and create some equations based on the provided angles and distances to solve this problem.

a) We can use the tangent function to calculate the separation between boat A and the lighthouse:

opposite/hypotenuse = tan(45°)

where the hypotenuse is the distance between boat A and the lighthouse, the other side is the lighthouse's height (i.e., the horizontal distance we want to find). By calculating the hypotenuse, we obtain:

Hypotenuse equals opposite/tan(45°) = 300/1 = 300 feet. Boat A is therefore 300 feet horizontally away from the lighthouse.

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Answer:

  (c)  42.9 ft²

Step-by-step explanation:

You want the area of the right triangle with hypotenuse 17.3 ft and long side 16.5 ft.

The Pythagorean theorem tells you the relationship between the side lengths is ...

  c² = a² +b²

The missing side, b, can be found as ...

  b² = c² -a²

  b = √(c² -a²) = √(17.3² -16.5²) = √27.04 = 5.2

The area of the triangle is ...

  A = 1/2bh

  A = 1/2(16.5 ft)(5.2 ft) = 42.9 ft²

The area of the triangle is 42.9 square feet.

So the lowest possible score to qualify for the police academy is 225.6.

In statistics, the mean is a measure of central tendency that represents the average value of a set of data. It is calculated by adding up all the values in the data set and then dividing by the total number of values.

Here,

To find the Z-score, you will need to use the following formula:

Z = (X - μ) / σ

where:

X = the raw score you are trying to find

μ = the population mean (in this case, 200)

σ = the population standard deviation (in this case, 20)

To find the lowest possible score to qualify, you need to find the score that corresponds to the 90th percentile (i.e., the top 10%).

To do this, you can use a standard normal distribution table or a calculator that has a normal distribution function.

Here are the steps:

Find the Z-score that corresponds to the 90th percentile.

You can use a standard normal distribution table to find this value. Look for the row that corresponds to the first digit(s) of the percentile (in this case, 9) and the column that corresponds to the second digit (in this case, 0.0). This will give you the Z-score that corresponds to the 90th percentile, which is approximately 1.28.

Alternatively, you can use a calculator that has a normal distribution function. For example, in Excel, you can use the formula =NORM.S.INV(0.9) to find the Z-score that corresponds to the 90th percentile.

Plug in the values for μ, σ, and Z into the formula for Z-score:

Z = (X - μ) / σ

Rearranging the formula, we get:

X = Z * σ + μ

Substituting the values we know, we get:

X = 1.28 * 20 + 200

X = 225.6

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The vertices of the image after the transformation are G' = (1, -3), H = (-3, -2), I' = (-1, -5) and J' = (-1, -1)

Given that

G = (1, -3), H = (5, -2), I = (3, -5) and J = (3, -1)

The reflection is given as

Reflection across x = 1

The rule of this reflection is

(x, y) = (-(x - 2a), y)

Where

Reflection across x = a = 1

So, we have

G' = (-(1 - 2), -3), H = (-(5 - 2), -2), I' = (-(3 - 2), -5) and J' = (-(3 - 2), -1)

Evaluate

G' = (1, -3), H = (-3, -2), I' = (-1, -5) and J' = (-1, -1)

Hence, the image of the reflection are G' = (1, -3), H = (-3, -2), I' = (-1, -5) and J' = (-1, -1)

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What are the coordnate of the reflection across x = 1 of GHIJ such that

G = (1, -3), H = (5, -2), I = (3, -5) and J = (3, -1)

Answer: I think line plot and bar graph

Step-by-step explanation:

Answer:

Let's begin by finding the total work required to complete the manuscript of the book:

Total work = (Number of typists) x (Number of hours per day) x (Number of days) = 6 x 5 x 16 = 480

Now let's find the work done by 4 typists working 6 hours per day:

Work done by 4 typists = (Number of typists) x (Number of hours per day) x (Number of days) = 4 x 6 x d

where d is the number of days required to complete the manuscript.

Since the amount of work done is the same in both cases, we can set the two equations equal to each other and solve for d:

6 x 5 x 16 = 4 x 6 x d

Simplifying this equation, we get:

480 = 24d

Dividing both sides by 24, we get:

d = 20

Therefore, it will take 4 typists working 6 hours per day a total of 20 days to complete the manuscript of the book.

Step-by-step explanation: