Which unit would be best for measuring the thickness of a coin?
I
kilometer
meter
millimeter
centimeter
Done

The line graph of the inequality is represented by an open circle at x = - 9 going towards negative infinity.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

The given inequality is x + 3 < - 6.

x < - 6 - 3.

x < - 9.

The line graph of the inequality will be represented as an open circle at

x = - 9 extending towards negative infinity because x is strictly smaller

than 9.

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Answer:

1. 1/3 or 1 red paint : 3 yellow paint

2. 3/1 or 3 or 3 yellow paint: 1 red paint

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

The equation should read    t = 2000/ (600-w)

   the asymptote will be at w = 600 as this would create a value of zero in the denoiminator....  when the windspeed approaches 600 the time to complete the flight approaches infinity as the windspeed subtracts from the 600 mph plane speed.....then the forward ground speed gets smaler and smaller approaching zero mph.

The T10 of the sequence is

T10 =-10.00

Generally, To determine the T10 of a geometric sequence, you will need to know the common ratio of the sequence.

If T2=-10 and

T6=-160, we can use these terms to find the common ratio.

The formula for any term in a geometric sequence is:

Tn = a * r^(n-1)

Where

We can use the terms you provided to find the common ratio:

-160 = -10 * r^(6-1)

-160 = -10 * r^5

r = (-160/-10)^(1/5)

Now that we know the common ratio, we can find T10:

T10 = a * r^(10-1)

T10 = -10 * r^9

So the T10 of the geometric sequence is

T10= -10 * (-160/-10)^(1/5)^9

T10 =-10.00

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The scale factor is 5 / 24. And the actual dimension A if A is 1.25 in will be 6 inches.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

The base of the flange shown in the drawing is actually 24 in. Its drawing width is 5 in.

The scale factor is given as,

Scale factor = 5 / 24

Then the actual dimension A if A is 1.25 in will be given as.

⇒ 1.25 / (5/24)

⇒ 1.25 x (24 / 5)

⇒ 6 inches

The scale factor is 5 / 24. And the actual dimension A if A is 1.25 in will be 6 inches.

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Answer:

$4.50 each

Step-by-step explanation:

27/6=4.50

Diameter of Lawn = 28 cm

Length of rope tied at the centre of lawn = 7cm.

As the cow, tied to the rope grazes the lawn it forms a circle with radius 7cm.

Area of lawn grazed by cow

= pi*7^2. ( pi = 3.14)

= 3.14 * 49

= 153.86 sq. cm

Area of the lawn with radius 14 cm

= pi * 14^2. (pi = 3.14)

= 3.14 * 14^2

= 615.44 sq cm

Remaining area = Area of the Lawn - Area of the lawn grazed by cow

= 615.44 - 153.86

= 461.58 sq cm

Answer:

Step-by-step explanation:

Answer:

420 millimeters

Step-by-step explanation:

If the scale factor of the enlargement is 70, and the body length of the insect is 6 millimeters, then the body length of the insect under the microscope is 6 millimeters * 70, which is 420 millimeters. So the correct answer is 420 millimeters.

The values sinθ=-5/√34, cosθ=-3/√34, tanθ = 5/3, cotθ = 3/5, secθ = -√34/3 and cscθ = -√34/5

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We have to find the values of sine, cosine, tangent, cosecant, secant, and cotangent for the angle θ in standard position on the coordinate plane with the point (−3,−5) on its terminal side

r=√9+25

=√34

sinθ=y/r

sinθ=-5/√34

cosθ=x/r

cosθ=-3/√34

tanθ = y/x

tanθ = 5/3

cotθ = x/y

cotθ = 3/5

secθ = r/x

secθ = -√34/3

cscθ = r/y

cscθ = -√34/5

Hence, values sinθ=-5/√34, cosθ=-3/√34, tanθ = 5/3, cotθ = 3/5, secθ = -√34/3 and cscθ = -√34/5

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The participant received a head start of 4 meters. The 4 in the equation represents the initial position of the participant.

The participant's rate of speed of the participant is 3 meters per second.

a. The participant received a head start of 4 meters.

The 4 in the equation represents the initial position (y-intercept, c) of the participant, so this is the head start that the participant received.

b. The participant's rate of speed of the participant is 3 meters per second.

This means that for every 1 second (represented by x in the equation), the participant covers a distance of 3 meters. So the participant's rate of speed is 3 meters per x second

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The distance covered by the car in 8 seconds of the journey is 100 meters.

The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.

Given:

Velocity (m/s) = 20, 15, 10, 5, 0

Calculate the distance as shown below,

[tex]Distance = velocity \times time[/tex]

Distance = 0 × 20 + 15 × 2 + 10 × 4 + 5 × 6 + 0 × 8

Distance = 0 + 30 + 40 + 30 + 0

Distance = 100 meter

Thus, the distance covered by the car is 100 meters.

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Chelsea is sewing handmade scarves she has 7 1/2 yards of material and needs 2 1/4 yards of material for each scarf, so the number of scarves can she make with the existing material = 3. This can be solved using the concept of fractions.

In mathematics, the portion or component of the complete item is represented by a fraction. It stands for the equal components of the whole. Both the numerator and denominator are components of a fraction. The top number is referred to as the numerator, while the bottom number is referred to as the denominator.

Total material = [tex]7\frac{1}{2}[/tex] yards

[tex]= 7\frac{1}{2} = 7 + \frac{1}{2} = \frac{15}{2}[/tex] yards

Materials required for each scarf = [tex]2\frac{1}{4}[/tex] yards

Number of scarfs she make with the existing material

= Total Material ÷ Material required for each scarf

= [tex]\frac{15}{2}[/tex] ÷ [tex]\frac{9}{4}[/tex]

= [tex]\frac{15}{2}[/tex] × [tex]\frac{4}{9}[/tex]

= [tex]\frac{10}{3}[/tex]

= [tex]3\frac{1}{3}[/tex] ≈ 3

Hence, the number of scarves can she make with the existing material = 3.

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Expression [tex]\frac{\sqrt[7]{x} ^{2} }{\sqrt[5]{ y^{3}} }[/tex] is equal to [tex]x^{2/7} /y^{-3/7}[/tex]

The correct option is 1.

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

Examples:

3x + 4y – 7,  4x – 10, etc.

Given expression is

[tex]\frac{\sqrt[7]{x} ^{2} }{\sqrt[5]{ y^{3}} }[/tex]

⇒[tex]x^{2.1/7} /y^{3.1/5}[/tex]

⇒[tex]x^{2/7} /y^{3/5}[/tex]

⇒[tex]x^{2/7} . y^{-3/5}[/tex]

Hence [tex]\frac{\sqrt[7]{x} ^{2} }{\sqrt[5]{ y^{3}} }[/tex]  is equivalent to      [tex]x^{2/7} /y^{-3/7}[/tex].

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a). The equation of a function h(x) as required to be determined is; h (x) = 20,000 (0.85)^x.

b). The function h (x) as required to be described in terms of the parent function f(x) is a dilation of the parent function using a scale factor of 20,000.

c). The difference between the values of the $12,000 and the $20,000 car is; $3549.6.

It follows from the task content that the equation of the function g (x) is given as;

g (x) = 12,000 (0.85)^x.

a). On this note, since the rate of depreciation is same for the $20,000 car too; it follows that the exponential function which represents the situation is;

h (x) = 20,000 (0.85)^x.

b). Also, since the parent function f (x) = 0.85^x, the function g(x) can be described relative to the parent function as a dilation of the parent function using a scale factor of; 20,000.

c). The value of the $12,000 item after 5 years is;

g (5) = 12,000 (0.85)⁵ = $5324.5.

Also, the value of the $20,000 car after 5 years is;

h ( 5 ) = 20,000 (0.85)⁵ = $8874.1.

On this note, the difference between the values of the two items is; 8874.1 - 5324.5 = $3549.6.

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The solution is

a) The measure of diagonal of rectangle BD = 24

b) The measure of ∠EBC of rhombus = 51°

c) The measure of EF of parallelogram = 17

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the diagonals of the rectangle ABCD intersect at E

The measure of AE = x + 4

The measure of CE = 3x - 12

Now , the measure of BD = 2AE

For a rectangle , the diagonals are equals

So , x + 4 = 3x - 12

On simplifying the equation , we get

Subtracting x on both sides of the equation , we get

2x - 12 = 4

Adding 12 on both sides of the equation , we get

2x = 16

Divide by 2 on both sides of the equation , we get

x = 8

Now , the measure of AE = x + 4 = 12

The measure of BD = 2AE = 2 x 12

The measure of BD = 24

b)

For a rhombus , the adjacent angles of a rhombus add up to 180° and the diagonals of a rhombus are perpendicular to each other

The measure of ∠EBC = 8a - 5

The measure of ∠ECB = 5a + 4

And , 2 (  measure of ∠EBC + measure of ∠ECB ) = 180°

2 ( 8a - 5 + 5a + 4 ) = 180°

On simplifying the equation , we get

Divide by 2 on both sides of the equation , we get

8a - 5 + 5a + 4 = 90

13a - 1 = 90

Adding 1 on both sides of the equation , we get

13a = 91

Divide by 13 on both sides of the equation , we get

a = 7

Now , substitute the value of a in m∠EBC , we get

The measure of ∠EBC = 8a - 5

The measure of ∠EBC = 8 ( 7 ) - 5

The measure of ∠EBC = 56 - 5 = 51°

Therefore , the measure of ∠EBC is 51°

c)

The median of a trapezoid is parallel to the bases and is one-half of the sum of measures of the bases

So ,

The measure of EF = ( 1/2 ) ( measure of DC + measure of AB )

Substituting the values in the equation , we get

2x + 1 = ( 1/2 ) ( 2x - 2 + 3x - 4 )

Multiply by 2 on both sides of the equation , we get

4x + 2 = 5x - 6

Subtracting 4x on both sides of the equation , we get

x - 6 = 2

Adding 6 on both sides of the equation , we get

x = 8

So , the measure of EF = 2x + 1

The measure of EF = 2 ( 8 ) + 1

The measure of EF = 17

Hence , the equations are solved

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An event that will have a sample space of S = {g, b} include the following: C. Flipping a two-sided coin with one side green and the other side blue.

In Mathematics and statistics, a sample space can be defined as a set or collection of possible outcomes (results or outputs) that are obtainable from a random experiment. Mathematically, a sample space is represented or denoted by using the symbol, "S."

Additionally, a sample space may contain a number of outcomes (results or outputs) that depends on the experiment. Generally speaking, the subset of possible outcomes (results or outputs) of that are obtainable from an experiment is typically referred to as events.

In this context, we can reasonably infer and logically deduce that "Flipping a two-sided coin with one side green and the other side blue" is an event which would have a sample space that is modeled by this mathematical expression;

S = {g, b}

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Answer: C: Flipping a two-sided coin with one side green and the other side blue.

The volume of the solid generated when R is rotated about the horizontal line y=-2 is 98.868.

The volume of the solid:3.574

The equation involving integral expressions:

[tex]\int\limits^k_0 {(4-f(x))} \, dx =\int\limits^2_0 {(4-f(x))} \, dx[/tex]

The given equation is f(x)=x^4-2.3x^3+4

f(x)=4 ⇒x=0,x=2.3

Now, substitute the values in the equation:

⇒ Volume=  [tex]\pi \int\limits^2_0 {(4-(-2)^2)} \, dx -(f(x)-(-2)^2)dx[/tex]

By solving the equation we get:

volume=98.868

b) consider the point r in the graph which is perpendicular to the x-axis that an isosceles right triangle with a leg in r.

Area of cross-section:

A=1/2(leg)(leg)=1/2(4-f(x))^2

Volume=∫(1/2(4-f(x))^2)dx     ∴with limits (0 to 2.3)

Solving the function we get:

Volume=3.574

c)given the vertical line x=k divides R into two regions with equal areas.

∫(4-f(x))dx=∫(4-f(x))dx

2∫(4-f(x))dx=∫(4-f(x))dx            ∴with limits 0 to 2.3 and 0 to k

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Answer:

1) 6 kids have hamsters

13 kids have dogs

2) Tia scored more in English

She scored around 15 points more

Her range is around 15

Step-by-step explanation:

Answer:

for the first three questions:

1. fill out two boxes in the cat section

2. 6 students

3. 13 students

for the last questions:

1. just fill the lines up to the numbers in the question

2. english

3. about 18%? (not sure)

Step-by-step explanation:

The total sales required to earn the desired income of $2800 is calculated to be $6,375.

Sale is a business transaction involving the exchange of goods or services for money. It can refer to the act of selling, or the thing that is sold. Sales are typically the main source of revenue for businesses. The process of selling involves finding potential customers, negotiating a price, and delivering the product or service. The ultimate goal is to make a profit.

In order to earn a monthly income of $2800, a local salesman would need to sell $6,375 worth of goods in a month. This is calculated by subtracting the base salary of $875 from the desired income of $2800, which leaves $2,925. Then, 6% of $1450 is $87, so the remaining $2,838 must be made up of 6% of the sales above $1450. By dividing this amount by 6%, the total sales required to earn the desired income of $2800 is calculated to be $6,375.

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Using strategic thinking, the solutions to the following questions are:

Strategic thinking involves using rational thought processes to focus on workable solutions to business problems.

Strategic thinking concentrates on the future based on its changing environments.

In this situation, 50% of a number represents one-half of the given value.  We can divide each number by 2 to find the solutions.

a) 50% of 10 liters of milk = 5 liters (10 x 50%)

b) 50% of 2,000 kilometers = 1,000 kilometers (2,000 x 50%)

c) 50% of 24 hours = 12 hours (24 x 50%)

Thus, strategically thinking, half of each value represents its 50%.

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Answer: both are proportional

Step-by-step explanation:

Both. ..............................

Answer:

a) 35 degrees

b) 98 degrees

Step-by-step explanation:

Complementary angles measure up to 90 degrees. So if one angle measures 55 degrees, the other would have to be 35 degrees as

55 + 35 = 90

Supplementary angles measure up to 180 degrees. So if one angle measures 82 degrees, the other would have to be 98 degrees as

82 + 98 = 180

On solving the provided question, we cam say that - by unitary method the answer is 4/5

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here, construction worker = 2/3 pounds

he has = 1/2

so the answer is 4/5

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The height of the doctor's office is solved using similar triangles to give

When the corresponding sides of two triangles are proportionate and their corresponding angles are congruent, The triangles are said to be similar.

As a result, the triangle's side should be proportionate if its corresponding angles are congruent.

Examining the descriptions shows that pair of equivalent sides are

height of tree and shadow of tree,

height of doctor's office and shadow's of doctor's office

The solution is worked out

height of tree / shadow of tree = height of doctor's office / shadow's of doctor's office

7 / 3 = height of doctor's office / 21

cross multiplying

3 * height of doctor's office = 7 * 21

height of doctor's office = 7 * 21 / 3

height of doctor's office = 49 feet

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The new volume of the cylinder is now 120 cubic feet.

Original volume = 10 cubic feet

Original radius = r

Original height = h

New radius = 2r

New height = 3h

New volume = V

V = π * (2r)^2 * 3h

 = π * 4r^2 * 3h

 = 120π cubic feet

 = 120 cubic feet

The original volume of the cylinder was 10 cubic feet. The radius of the cylinder was doubled and its height was tripled. Therefore, the new radius is twice the original radius and the new height is three times the original height. The new volume of the cylinder can be calculated using the formula V = π * (2r)^2 * 3h. This gives us a new volume of 120 cubic feet.

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If the radius of the cylinder is doubled and its height is tripled , then the new volume of the cylinder will be 120 cubic feet .

The Volume of the cylinder is calculated by the formula , V = πr²h ,

where r is the radius and h is height ,

the volume (V) of the cylinder is = 10 cubic feet ,

given that the radius is doubled , and height is tripled ,

So , we substitute r = 2r and h = 3h ,

Let V' be the volume of the new cylinder ,

We get , V' = π(2r)²(3h)

= π × 4r² × 3h

= 12πr²h

= 12 × V ,

substituting V = 10 ,

we get ,

V' = 120 cubic feet .

Therefore , the volume of the new cylinder is 120 cubic feet .

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a) The values of c and d are 7 and 58.

b) The coordinates of the turning point of the curve y = -x² - 14x + 9 is,

⇒ (- 7, 58)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The expression is,

⇒ - x² - 14x + 9

Now, Simplify the expression to change in the form of -(x + c)² + d as;

⇒ - x² - 14x + 9

⇒ - (x² + 14x) + 9

⇒ - (x² + 14x) - 49 + 49 + 9

⇒ - (x² + 14x + 49) + 49 + 9

⇒ - (x + 7)² + 58

By comparing, we get;

The values of c and d are,

⇒ c = 7

⇒ d = 58

And. To find the coordinates of the turning point of the curve

y = -x² - 14x + 9, we can differentiate it with respect to x and equate it to zero.

⇒ y = -x² - 14x + 9

⇒ dy/dx = - 2x - 14 = 0

⇒ - 2x = 14

⇒ x = - 7

And,

⇒ y = -x² - 14x + 9

⇒ y = - (-7)² - 14×- 7 + 9

⇒ y = - 49 + 98 + 9

⇒ y = 58

Thus, The coordinates of the turning point of the curve y = -x² - 14x + 9 is,

⇒ (- 7, 58)

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Each side length of an equilateral triangle is (6x³+9x)/3  units

What is perimeter?

The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.

An equilateral triangle has all the sides equal in length

Let each side be y

Perimeter is the sum of all sides

So, Perimeter = y+y+y = 3y

Given, Perimeter = 6x³+9x

=> 3y= 6x³+9x

=> y= (6x³+9x)/3  

Thus, each side length of an  equilateral triangle is (6x³+9x)/3  units

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