The largest possible circle is cut out of a square whose side length is 8 feet. What will be the approximate area, in square feet, of the remaining board? ( where

Answer:

8:36

Step-by-step explanation:

Answer:

Step-by-step explanation:

2/8

To find the percentage of the shaded area inside the square, we need to determine the area of the shaded region and calculate the percentage relative to the total area of the square. Without more information or measurements, we can't determine the exact size of the shaded area or the percentage.

To find the percentage of the area inside the square that is shaded, we need to determine the area of the shaded region and then calculate the percentage. Given the perimeter of the square is 40cm, we can find the length of each side by dividing the perimeter by 4, which gives us 10cm. The area of the square is found by squaring the length of one side, so the area is 10cm x 10cm = 100cm². To find the shaded area, we need to subtract the area of the square from the total area. Assuming the shaded region is a smaller square with side length x, the area of the shaded region is x². So the shaded area is 100cm² - x².

To calculate the percentage, we divide the shaded area by the total area of the square and multiply by 100. So the percentage of the area inside the square that is shaded is (100cm² - x²) / 100cm² * 100.

It's important to note that we don't have enough information to determine the exact size of the shaded area or calculate the percentage without more details or measurements of the shaded region.

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Answer(s): 1/2, 1, 1/3, 1/4

Any of these could work. Any number beyond 1 could work. The fraction 1/12 is pretty small, and the bigger the number in fractions, the smaller they get.

Example: 1/24 is bigger than 1/64

Because 64 is a bigger number, you'd have to cut it up more and more, getting smaller pieces.

So,  any number smaller than 12 in a fraction could work- EXCEPT negatives. All whole numbers work as well.

Answer:

Step-by-step explanation:

[tex]15a\geq 75\\15(5)\geq75\\75\geq75\\True[/tex]

If we substituted 1 for a then:

[tex]15a\geq75\\15(1)\geq75\\15\geq75\\False[/tex]

Answer:

4/7

Step-by-step explanation:

you just flip the numbers across the division/fraction sign

Heya.

First, let us learn about reciprocals.

Basically, it's the fraction flipped. Easy as 1, 2, 3!

Let's do an example:

We have an equation that says Find the reciprocal of 5/2.

1. Flip the fraction.

2. We then have 2/5 as a final answer.

Now onto the question:

1. We need to flip the equation.

2. This results as 4/7.

Therefore, our answer is "4/7".

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Height of the trapezoid is 14.4 meter.

Solution:

Given data:

One base [tex](b_1)[/tex] = 12 meter

Other base [tex](b_2)[/tex] = 8 meter

Area = 144 square meter

Area of the trapezoid = [tex]\frac{1}{2} \times(b_1+ b_2)\times h[/tex]

[tex]$144=\frac{1}{2} \times(12+8)\times h[/tex]

[tex]$144=\frac{1}{2} \times 20 \times h[/tex]

[tex]$144= 10 \times h[/tex]

Divide by 10 on both sides, we get

14.4  =  h

Switch the sides of the equation.

h = 14.4

Height of the trapezoid is 14.4 meter.

The graph of g(x) = f(–2x) will be a horizontally stretched and reflected version of the graph of the parent function f(x) = x^3. The reflection occurs over the y-axis, and the stretch is by a factor of 1/2.

The student's question involves a transformation of a cubic parent function. The original function, f(x) = x3, represents a standard cubic graph, which is symmetric about the origin and increases from negative infinity to positive infinity as x does the same. The transformation g(x) = f(–2x) modifies the parent function in two notable ways. First, the multiplication by –2 reflects the graph over the y-axis (because of the negative sign) and also stretches it horizontally by a factor of 1/2 (because the absolute value of the number is greater than 1).

To visualize this, if we consider specific points on the graph of f(x) such as (1,1), (2,8), and (3,27), you would find their corresponding points on g(x) at (-0.5,1), (-1,8), and (-1.5,27), respectively. This indicates that every point on g(x) is twice as far from the y-axis as it is on f(x), and on the opposite side due to the reflection.

The effect of this transformation demonstrates the result of horizontal stretching and reflection when contrasts with the original function f(x), providing insight into how linear transformations affect the shape and position of graphs.

Answer:

The answer is:

No, they are not independent because P(student)≈ 0.82 and P(student|pirate) ≈0.94

Step-by-step explanation:

so the answer is B

No, they are not independent because P(student) = 0.82 and P(Student|pirate) = 0.94

The probability of being student P(student) = 0.82

The probability of perferring pirate P(pirate) = 0.94

These two events are not independent events.

Hence, they are not independent because P(student) = 0.82 and P(Student|pirate) = 0.94

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Answer: Area is 168ft^2

Step-by-step explanation:

Answer:

D) 50ft

Step-by-step explanation:

(18×x) + (32×18) + [(48-18-18)×(32-11)]

= 1728

18x + 576 + (12×21) = 1728

18x = 1728 - 828

18x = 900

x = 50

Answer:

11+(2×4)

11+8

$19....

Answer:

Cost for 2 hours=19, Cost for 2 hours=11+4t

72 = l . w . h

72 = x . (x - 1) . (x + 9)

72 = (x² - x) . (x + 9)

72 = x³ + 9x² - x² - 9x

72 = x³ + 8x² - 9x

0 = x³ + 8x² - 9x - 72

0 = x² (x + 8) - 9 (x + 8)

0 = (x² - 9)(x + 8)

0 = (x - 3)(x + 3)(x + 8)

x = 3 or x = -3 or x = -8

so, x = 3

length = x = 3

width = x - 1 = 2

height = x + 9 = 12

Final answer:

To find the dimensions of the rectangular prism, set up an equation using the volume formula and solve for x. The dimensions of the box are 3 feet, 2 feet, and 12 feet.

Explanation:

To find the dimensions of the box, we need to set up an equation using the volume formula for a rectangular prism. The volume of a rectangular prism is given by V = length x width x height.

So, we have the equation x(x - 1)(x + 9) = 72.

Simplifying this equation, we get x³ + 8x² - 9x - 72 = 0.

Using factoring or synthetic division, we find that x = 3 is a solution to the equation. Therefore, the length of the box is 3 feet, the width is 2 feet, and the height is 12 feet.

Answer:

C. $5.55

Step-by-step explanation:

Total cost of installing 60 square feet of flooring

= $253.00 + $80

= $333

Total number of square feet for flooring = 60

Now cost per square foot of the flooring

= total cost/total number of square feet

That’s

$333/60 = $5.55

Each square foot cost $5.55

The resulting coordinate of X is (0, -2)

Given the coordinate point X (-3, -2). If the coordinate is translated using the rule (x, y) = (x+3, y + 4), the resulting coordinate will be (-3+3, -2+4) = (0, 2)

In conclusion, the resulting coordinate of X is (0, -2)

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After translation and reflection, the coordinate of X" is (0, -2).

To find the coordinate of X" after a translation and reflection, we need to first apply the translation rule to point X (-3, -2). Using the rule (x, y) = (x+3, y + 4), we add 3 to the x-coordinate and add 4 to the y-coordinate:

x' = -3 + 3 = 0

y' = -2 + 4 = 2

After the translation, the new coordinates are (0, 2). To reflect over the x-axis, we change the sign of the y-coordinate, giving us the final coordinate of X" as (0, -2).

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Solution:

Distance between two points is given by:

[tex]d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}[/tex]

We have to find the distance in the standard (x, y) coordinate  plane between the points (2,3) and (5,5)

From given,

[tex](x_1, y_1) = (2, 3)\\\\(x_2, y_2) = (5, 5)[/tex]

Substituting the values we get,

[tex]d = \sqrt{(5-2)^2 + (5-3)^2}\\\\Simplify\\\\d = \sqrt{3^2 + 2^2}\\\\d = \sqrt{9+4}\\\\d = \sqrt{13}\\\\In\ decimal\ form\\\\d = 3.605 \approx 3.6[/tex]

Thus distance between the points (2,3) and (5,5) is 3.6 units

The distance between the points (2,3) and (5,5) on the standard (x, y) coordinate plane is determined using the distance formula. After substituting the given coordinate points into the formula, we find that the distance is √13 units.

In Mathematics, the distance between two points in the (x, y) coordinate plane is given by the distance formula, which is √[(x₂-x₁)² + (y₂-y₁)²]. This formula is acquired from the Pythagorean theorem. Here, the points are (2,3) and (5,5). So, substituting these values in the distance formula, we get:

Distance = √[(5-2)² + (5-3)²] = √[3² + 2²] = √[9+4] = √13.

Therefore, the distance between the two points (2,3) and (5,5) on the standard (x, y) coordinate plane is √13 units.

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Answer:

The penny has a circuferance of  2.356194

Step-by-step explanation:

To get this I used the formula for circumference c = πd or c = 2π x r²

And you just plug in 0.75 for d and multiply it by 5 to get you answer

The circumference of the penny is approximately 2.36 inches.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The circumference of a circle is expressed mathematically as;

Circumference = 2πr or dπ

Where r is the radius, d is the diameter, and π is constant pi.

Given the parameter:

Diameter of the penny d = 0.75 inches

Circumference =?

To find the circumference of the penny, we can use the formula for the circumference of a circle.

Circumference = dπ

Plug in the diameter values:

Circumference = 0.75 × π

Circumference = 0.75π in or 2.36 in.

Therefore, the circumference is approximately 2.36 inches.

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Hello, remember you need to write complete questions in order to get good and exact answers. Here you haven't provided any fractions, so I'll give you my own fractions.

The first fraction is:

[tex]\frac{1}{2}[/tex]

The second fraction is:

[tex]\frac{1}{4}[/tex]

So let's say that difference is:

[tex]\frac{1}{2}-\frac{1}{4}[/tex]

Therefore, the result is:

[tex]\frac{1}{2}-\frac{1}{4}=\frac{1}{4}[/tex]

The representation of this problem is shown using the number line below. As you can see, we have written both 1/2 and 1/4 and the difference is also indicated giving the result 1/4. That is, if we walk from 1/4 to 1/2 we'll walk 1/4 units.

Answer:

-7/10

Step-by-step explanation:

Bruh trust me

Answer:

2h+3 Because they bought 2 hot dogs and h represents the amount they cost. And the 3 represents the drink he purchased

Answer:

144 pounds

Step-by-step explanation:

Weight of object Earth: Weight of Object Planet B

100:3 = 4800:b

100/3=4800/b

100b=14400

b=144

Therefore, 144 pounds

The weight of an elephant on planet B can be calculated using the weight ratio of 100 (on Earth) to 3 (on planet B). By setting up a proportion and solving for the unknown weight, we find that the elephant weighs 144 pounds on planet B.

Since the ratio is 100 to 3, we can set up a proportion to find the elephant's weight on planet B.

First, represent the known weight ratio between Earth and planet B: 100 (earth weight) to 3 (planet B weight).

Then, set up the proportion using the weight of the elephant on Earth (4,800 pounds) and let x represent the unknown weight on planet B:

100/3 = 4800/x

To solve for x, cross-multiply and divide:

100x = 4800 * 3

Finally, divide both sides by 100 to find x:

x = (4800 * 3) / 100

x = 144 pounds

Therefore, the elephant would weigh 144 pounds on planet B.

Answer:

A) For line l = (2x + 8°) + (5x - 10°) = 180° ....... (i)

For line k = (3x + 42°) + (x + 34°) = 180° ....... (ii)

B) In line l, two angles are = 60° and 120°

In line k, two angles are =  120° and 60°

Step-by-step explanation:

Requirement A

To find the measure of each angle, we have to use equation.

According to the graph, line l and k are parallel, therefore, both are straight angle. We know that a straight angle is equal to 180°. Therefore, line l and k are 180°. As both the line are intersected by line j, the lines are separated by two angles. So, the equation for line l is -

(2x + 8°) + (5x - 10°) = 180° ....... (i)

the equation for line k is -

(3x + 42°) + (x + 34°) = 180° ....... (ii)

Requirement B

For line "l "

By solving the equations, we can measure the angles

(2x + 8°) + (5x - 10°) = 180°

or, 2x + 8° + 5x - 10° = 180°

or, 7x - 2° = 180°

or, 7x = 180° + 2°

or, 7x = 182°

or, x = 182° ÷ 7 [Dividing both the sides by 7]

or, x = 26°

Therefore, 2x + 8° = 2 × 26° + 8° = 52° + 8° = 60°

the other angle is = 5x - 10° = 5 × 26° - 10° = 130° - 10° = 120°

For line "k "

(3x + 42°) + (x + 34°) = 180°

or, 3x + 42° + x + 34° = 180°

or, 4x + 76° = 180°

or, 4x = 180° - 76° [Deducting 76° from the both the sides]

or, 4x = 104°

or, x = 104° ÷ 4

Hence, x = 26°

Therefore, 3x + 42° = 3 × 26° + 42° = 78° + 42° = 120°

The other angle is = x + 34° = 26° + 34° = 60°

Answer: Amount of change : $30

percent increase : 200%

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

To obtain the amount of change we have to subtract the wholesale price to the retail price:

Mathematically speaking:

45 -15 = $30

For the percent increase, the amount of change (30) is some percent of the original price (15). So:

30 / 15 =2 (decimal form)

If we multiply it by 100, the percentage is:

200%

Answer:

Step-by-step explanation:

(4x^2-2x+8)+(x^2+3x-2)

Collect like terms

5x^2+x+6

5x^2+x+6 dont know if you need to siplify it any more

Answer:

n = 3

Step-by-step explanation:

Equation:  17.1 = 5.7 * n

Divide both sides by 5.7 to get n by itself.

Step 1:  Divide both sides by 5.7

17.1 = 5.7 * n

17.1 / 5.7 = 5.7 * n / 5.7

    divide            divide

3 = n

Answer:  n = 3

We are given the following equation and want to solve for the unknown variable, n:

[tex]17.1=5.7 \times n[/tex]

To solve for an unknown variable, we want to isolate the variable by doing operations to both sides of the equation:

For this equation, we'll divide both sides by 5.7 to isolate the unknown variable n

[tex]17.1 \boxed{\div 5.7} = 5.7 \times n \boxed{\div 5.7}[/tex]

After dividing both sides by 5.7 and simplifying, we get:

[tex]3=n[/tex]

The next step is a bit tedious, but in math, you usually want to have the variable on the LEFT side of the equation after isolation.

After reversing the equation accordingly, we have:

[tex]\boxed{n=3}[/tex]

We have a value for n, which is 3.

Let me know if you need any clarifications, thanks!

~ Padoru

Answer:

D

Step-by-step explanation:

Answer:

The scale factor of the dilation is 3

Step-by-step explanation:

we know that

A dilation is a non rigid transformation that produce similar figures

so

Rectangle ABCD and rectangle A'B'C'D' are similar

Remember that

If two figures are similar, then the ratio of its corresponding sides is proportional

Let

z ----> the scale factor

[tex]z=\frac{D'C'}{DC}[/tex]

we have

[tex]D'C'=12-3=9\ units[/tex] ----> difference of x-coordinates

[tex]DC=4-1=3\ units[/tex]  ---> difference of x-coordinates

substitute

[tex]z=\frac{9}{3}=3[/tex]

The scale factor is greater than 1

so

The dilation is a enlargement

Answer:

1. 6100

2. 1150

3. 60

4. 50

Step-by-step explanation:

yes is an equilateral triangle also a rhombus

Answer:

ues it is   a equilateral triangle

Step-by-step explanation:

from the meaning of equilateral, equilateral means all sides are equal in length.

a rrhombus has all its side equal.and therefore it s an  equilateral triangle

Answer:

54π in³

Step-by-step explanation:

The volume (V) of a cylinder is calculated as

V= πr²h ( r is the radius and h the height )

Here r = 3 and h = 6, thus

V = π × 3² × 6 = π × 9 × 6 = 54π in³

Answer:

[tex]486\ in^2[/tex]

Step-by-step explanation:

we know that

The surface area of the cube is equal to the area of its six square faces

so

[tex]SA=6b^2[/tex]

where

b is the length side of the cube

we have

[tex]b=9\ in[/tex]

substitute

[tex]SA=6(9)^2=486\ in^2[/tex]

Answer:

486

Step-by-step explanation: