A circle has diameter 6 cm. Calculate the area of the circle. Give the units of your answer.​

The slope is 4 over 5, which means for each additional donut sold, the shop is predicted to earn $0.80.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The manager of the shop gathered data from several donut shops in the city for the total cost, y, for different amounts of donuts, x.

Now, Let two point on the line are (3, 3) and (8, 7).

Hence, The value of slope is,

Slope = (7 - 3) / (8 - 3)

Slope = 4/5

Thus, We get;

The slope is 4 over 5, which means for each additional donut sold, the shop is predicted to earn $0.80.

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According to the Centers for Disease Control and Prevention (CDC) growth charts, the average height for a 14-year-old guy in the United States is about 5 feet, 5 inches (165 cm). Some 14-year-old guys may be taller or shorter than the average.

Height is a measure of the distance between the base of an object and its highest point. Human height is commonly described as the vertical distance between the bottom of the feet and the top of the head. Height is generally measured in centimetres or feet and inches. Height is an important physical feature that can be influenced by both inherited and environmental factors such as nutrition and physical activity.

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To convert cm to inches, divide your cm figure by 2.54 or multiply it by 0.3937. There are 2.54 cm in 1 inch.

So, 40 inches * 2.54 cm/inch = 101.6 cm

A centimeter (cm) is a decimal fraction of the meter, the System of UnInternational its (SI) unit of length, approximately equivalent to 39.37 inches.

To calculate a value in inches to the corresponding value in centimeters, just multiply the quantity in inches by 2.54 (the conversion factor).

Here is the formula:Value in centimeters = value in inches × 2.54There are 101.6 cm in 40 inches.This can be calculated by using the conversion factor of 1 inch equals 2.54 cm.

So, 40 inches can be converted to centimeters by multiplying 40 by 2.54:

40 inches * 2.54 cm/inch = 101.6 cm

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Answer:

There are 2 iron (Fe) atoms, 3 oxygen (O) atoms, and 3 carbon (C) atoms on both the reactant and product side of the equation. Therefore, the equation is balanced.

Answer:

There is 2 Iron(Fe) atoms , 6 Oxygen atoms and 3 carbon atom on both side so this equation is balanced I believed.

Answer:

I would assume that 100 would be 100 minutes in the air, if -100 represents 100 minutes before take-off.

Step-by-step explanation:

The magnitude of -v is [tex]\sqrt{(89)}[/tex]

In physics and mathematics, magnitude refers to the size or quantity of a physical or mathematical property. It can be represented by a scalar value or a vector with a scalar magnitude.

In the case of scalar magnitude, it represents a property's absolute value, which is always positive. For example, the magnitude of a force, velocity, or acceleration represents its absolute value without any direction.

In contrast, vector magnitude represents the length or size of a vector, including both its magnitude and direction. It can be calculated using the Pythagorean theorem, where the magnitude of a vector V with components (Vx, Vy, Vz) is:

[tex]|V| = sqrt(Vx^2 + Vy^2 + Vz^2)[/tex]

The magnitude of a vector is always positive and can be used to determine the distance between two points in space.

Overall, magnitude is an essential concept in many fields, including physics, mathematics, engineering, and computer science, and it plays a crucial role in understanding various physical and mathematical phenomena.

The magnitude of a vector is its length, which is calculated using the Pythagorean theorem. For a vector v = (a, b), the magnitude is given by:

[tex]|v| = sqrt(a^2 + b^2)[/tex]

The negative of a vector simply reverses its direction, but not its magnitude. Therefore, the magnitude of -v is the same as the magnitude of v.

Using this information, we can calculate the magnitude of -v as follows:

[tex]|-v| = |-( -5, 8)| = |(5, -8)|\\\|-v|\ = \sqrt{(5^2 + (-8)^2)} = \sqrt{(25 + 64) }= \sqrt{(89)}Therefore, the magnitude of -v is \sqrt{(89)}[/tex]

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The expression below are correct:

πr_c^2h_c / 4 = πr_p^2h_p / 5

h_c / h_p = (r_p / r_c)^2 * (5 / 4)

To prove that the equation

πr_c^2h_c / 4 = πr_p^2h_p / 5

and

h_c / h_p = (r_p / r_c)^2 * (5 / 4)

are correct, we can use some algebraic manipulation and the properties of ratios.

Starting with the first equation, we can simplify it as follows:

πr_c^2h_c / 4 = πr_p^2h_p / 5

5πr_c^2h_c = 4πr_p^2h_p (multiply both sides by 20 to get rid of fractions)

5r_c^2h_c = 4r_p^2h_p (cancel out π on both sides)

Next, we can rearrange the second equation to solve for h_c:

h_c / h_p = (r_p / r_c)^2 * (5 / 4)

h_c = h_p * (r_p / r_c)^2 * (5 / 4) (multiply both sides by h_p)

Now we can substitute this expression for h_c into the simplified version of the first equation:

5r_c^2h_c = 4r_p^2h_p

5r_c^2(h_p * (r_p / r_c)^2 * (5 / 4)) = 4r_p^2h_p (substitute h_c)

5r_c^2r_p^2(5/4) = 4r_p^2h_p (simplify)

5r_c^2 = (16/25)h_p (divide both sides by 4r_p^2)

Finally, we can substitute this expression for h_p into the earlier expression we found for h_c:

h_c = h_p * (r_p / r_c)^2 * (5 / 4)

h_c = (5/16)r_c^2 (substitute for h_p)

h_c / r_c^2 = 5/16

This means that the ratio of the height to the radius squared for cylinder c is 5/16, which is a constant value. We can also rearrange the simplified first equation to solve for h_p in terms of r_c and r_p:

5r_c^2h_c = 4r_p^2h_p

h_p = (5/4)h_c(r_c/r_p)^2 (divide both sides by 4r_p^2 and multiply by 5/4)

Substituting this expression for h_p into the second equation, we get:

h_c / h_p = (r_p / r_c)^2 * (5 / 4)

h_c / ((5/4)h_c(r_c/r_p)^2) = (r_p / r_c)^2 * (5 / 4) (substitute for h_p)

1 / ((5/4)(r_c/r_p)^2) = (r_p / r_c)^2 * (5 / 4) (simplify)

Now we can simplify this expression using the fact that (r_p / r_c)^2 = 1 / (r_c / r_p)^2:

1 / ((5/4)(r_c/r_p)^2) = (1 / (r_c/r_p)^2) * (5/4)

1 / (5/4) = (r_c/r_p)^4 * (5/4)

4/5 = (r_c/r_p)^4

(r_c/r_p)^2 = √(2/√5) or -(√2/√(√5))

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This value is approximate. The more accurate answer is roughly 266.66667 square feet but even this value is approximate as well.

========================================================

Explanation:

The scale of 1:40 means 1 inch on paper corresponds to 40 inches in real life. This type of notation is typically found on maps in the bottom corner.

What we'll do is multiply by 40 to go from the measurement on paper to the measurement in real life.

In short,

From here we multiply the length and width to get the area.

area = length*width

= 20*13.333

= 266.66 which rounds to about 267 square feet.

Feel free to round to some other level of precision. I'm rounding to the nearest square foot because that's the typical precision when it comes to listing sizes of houses and apartments.

Answer:not real

Step-by-step explanation:

Answer:

when the input t is -7, the output k is -89.

Using the equation k = 10t - 19 and substituting t = -7, we have:

k = 10(-7) - 19

k = -70 - 19

k = -89

Therefore, when the input t is -7, the output k is -89.

A volume of 2 liters is needed to obtain a 92 % solution.

In this problem we need to determine the volume of pure acid to be added with a volume of four liters of 88 % acid solution to get a 92 % solution. This can be done by definition of weighted average:

(88 / 100) · (4 L) + (100 / 100) · V = (92 / 100) · (4 L + V)

Where V is the volume needed of the pure acid, in liters.

3.52 L + V = 3.68 L + 0.92 · V

0.08 · V = 0.16 L

V = 2 L

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Answer:

Step-by-step explanation:

The 2.8 liter is refers to the engine's displacement or volume

In the context of an engine, "2.8 liter" typically refers to the engine's displacement or volume. Specifically, it means that the engine can hold 2.8 liters (or 2,800 cubic centimeters) of air and fuel mixture in its cylinders.

The displacement of an engine is an important factor in determining its power and performance characteristics, as it influences the amount of air and fuel that can be burned during each engine cycle.

Generally, larger engine displacements are associated with more power and torque, although other factors such as the engine's design and technology also play a role.

Therefore, 2.8 liter is engine displacement

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The diameter of the circle is 30 units, and the equation is:

(x + 3)^2 + (y - 3)^2 = 15^2

We know that the diameter of the circle is defined by the points (12, 3) and (-18,3)

Notice that the y-value is the same one in both points, then the diameter is the difference between the x-values:

d = 12 - (-18) = 30

The diameter is 30 units.

Then the radius, half the diameter, is 15 units.

To write the circle equation we need to find the center.

Because of the points (12, 3) and (-18,3) we know that the y-value of the center must be y = 3.

And the x-value is the midpoint between x = -18 and x = 12, that is:

x = (-18 + 12)/2 = -6/2 = -3

The center is at (-3, 3)

Remember that the equation for a circle of center (a, b) and radius R is:

(x - a)^2 + (y - b)^2 = R^2

Here the center is (-3, 3) and the radius is 15, so the equation is:

(x + 3)^2 + (y - 3)^2 = 15^2

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Percent difference is a measure of the relative difference between two values, expressed as a percentage.

It is determined as follows:

% difference = |(Value 1 - Value 2) / (Average of Values 1 and 2)| x 100%

where:

Assume that the value of a quantity in 2019 is 100 and that the same amount in 2020 is 120. The percentage difference between these two values is determined as follows:

Percent difference = |(100 - 120) / ((100 + 120) / 2)| x 100%

= |(-20) / (220 / 2)| x 100%

= 9.09%

This signifies that the quantity's value increased by 9.09% between 2019 and 2020. If the percentage difference is negative, it signifies that the quantity's value has fallen by that proportion.

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Not necessarily. It is true that if a function F is differentiable at a point A, then F must be continuous at A. This is one of the basic properties of differentiable functions.

However, the converse is not necessarily true. A function can be continuous at a point A without being differentiable at A. In fact, there are many examples of such functions, such as the absolute value function f(x) = |x| at x = 0, which is continuous but not differentiable at x = 0.

To see why a function can be continuous at a point A without being differentiable at A, let's consider the definition of continuity and differentiability.

A function F is continuous at a point A if and only if:

F(A) is defined.

The limit of F(x) as x approaches A exists.

The limit of F(x) as x approaches A is equal to F(A).

Therefore, we can conclude that if a function F is continuous at a point A, we cannot infer that F is differentiable at A.

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Is it true if F is continuous at A then F is differentiable at A?

Answer:

V = [tex]40in^{3}[/tex]

Step-by-step explanation:

V = [tex]\frac{lwh}{3}[/tex]= [tex]\frac{5*4*6}{3}[/tex]= [tex]40in^{3}[/tex]

Answer:

It will take about 13.5 years for the money to grow to $5,500
That would be about 13 years and 6 months

Step-by-step explanation:

The formula for accrued amount(principal + interest) is given by:
[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}\quad(1)\\[/tex]

where
P = Principal amount
r = R/100 where R is the annual interest rate as a percentage
n= number of times compounded per year
t = number of years

Given

A = $5,600
P = $3,500
R = 3.35% ==> r = 3.35/100 = 0.0335
n = 12 (since there are 12 months in a year)

We have to find out t

Plugging known values into equation (1)

[tex]5500 = 3500\left(1+ \dfrac{0.0335}{12}\right)^{12t}\\\\5500 = 3500 \left(1+ 0.002791\right)^{12t}\\\\5500 = 3500 (1.002791)^{12t}[/tex]

Switch sides so unknown appears on the left side:
[tex]3500 (1.002791)^{12t} = 5500[/tex]

Divide by 3500 both sides:
[tex](1.002791)^{12t} = \dfrac{5500 }{3500}\\\\(1.002791)^{12t} = 1.5714\\\\[/tex]

Take logs on both sides:
[tex]\ln \left(1.002791^{12t}\right)=\ln \left(1.5714\right)\\\\[/tex]

We have
[tex]\ln \left(1.002791^{12t}\right) = 12t\ln \left(1.002791\right)\\\\[/tex]

Therefore we get
[tex]12t\ln \left(1.002791\right)=\ln \left(1.5714\right)\\\\t\ln \left(1.002791\right)=\ln \left(1.5714\right)\\\\\\[/tex]

Dividing both sides by [tex]12\ln \left(1.002791\right)[/tex] this works out to
[tex]t=\dfrac{\ln \left(1.5714\right)}{12\ln \left(1.002791\right)}[/tex]

[tex]t = 13.51359\; years[/tex]

Rounding to one decimal place
[tex]t = 13.51\; years\\[/tex]

This would be roughly 13 years and 6 months

The conversion from mililitres to litre will be done using the relation between the two, where 1 liter has 1000 mililitres.

Firstly know the abbreviations. In this question, ml represents mililitres. Now, The mentioned problem is from unit conversion. As we know the relation, that one litre contains 1000 milliliters of any fluid. So, this is the method of conversion from mililitres to litre.

We can understand given conversion through example. Let us say Zainab has a bottle of 2000 mililitres. Now how many litres of liquid can this bottle contain?

1000 mililitres is present in 1 liter

So, 2000 mililitres will contain = 2000/1000

Performing division

2,000 mililitres will contain 2 litre liquid.

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2030 military time is equivalent to 8:30 PM in standard 12-hour time notation.

2030 is a military time notation for 8:30 PM in standard 12-hour time notation.

In military time, the 24-hour clock is used, where the first two digits indicate the hour and the last two digits indicate the minutes. The hour digits range from 00 to 23, and the minute digits range from 00 to 59.

To convert 2030 military time to standard 12-hour time notation, you can use the following steps:

Check if the hour digits are greater than 12. If the hour digits are 13 or higher, subtract 12 from the hour digits to get the equivalent hour in standard time notation.

Add "PM" after the hour and minute digits to indicate that it is in the evening.

Using these steps, we can convert 2030 military time to 8:30 PM in standard time notation:

Since the hour digits 20 are greater than 12, we subtract 12 from 20 to get 8.

Add "PM" after 8:30 to indicate that it is in the evening.

Therefore, 2030 is 8.30 PM

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The length of a pendulum with period 8 seconds would be, 316 feet.

What is Period of a simple pendulum?

The formula for the period T of a pendulum is T = 2π Square root of √L/g, where L is the length of the pendulum and g is the acceleration due to gravity.

The equation relating the period T and length L of a pendulum is given by:

T = 2π√(L/32)

We can rearrange this equation to solve for L in terms of T:

L = 32(T/2π)²

To find the length of a pendulum with period 8 seconds, we can substitute T = 8 into the above equation and solve for L:

L = 32(8/2π)²

L ≈ 316 feet

Rounding this value to the nearest foot, we get:

L ≈ 316 feet (to the nearest foot)

Therefore, The length of a pendulum with period 8 seconds would be, 316 feet.

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Therefore, the vertices of ∆A'B'C' are located at (-18, -18), (-6, 12), and (0, -24), and the answer is not listed among the given options.

A triangle is a geometric shape that consists of three line segments or sides that intersect at three points called vertices. The interior angles of a triangle always add up to 180 degrees, and the side opposite to the largest angle is the longest side, which is called the hypotenuse. Triangles are commonly used in geometry and in many branches of mathematics, as well as in real-world applications such as engineering, architecture, and physics.

Here,

To reflect ∆ABC over the x-axis, we need to negate the y-coordinates of each vertex. Then, to dilate the reflected triangle by a scale factor of 3 about the origin, we need to multiply each coordinate by 3.

The coordinates of the reflected triangle will be (-6, -6), (-2, 4), and (0, -8). Multiplying each coordinate by 3, we get (-18, -18), (-6, 12), and (0, -24).

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The chances of Renata being ready to complete kindergarten tasks when she enters school are about 1/2. The solution has been obtained by using the concept of probability.

What is probability?

To calculate the chance of an event, use the mathematical notion of probability. It only enables us to estimate the likelihood that an event will take place. On a scale of 0 to 1, where 0 represents impossible and 1 represents a certain event.

We are given that Renata is a 5-year-old girl from a poor family in the united states, who is about to enter kindergarten.

The chances of Renata being ready to complete kindergarten tasks when she enters school are about 1/2 because it is not necessary that she will be able to do all the tasks. She might be able to do and she might not be able to do.

So, there are equal chances of both.

Hence, chances of Renata being ready to complete kindergarten tasks are 1/2.

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Division by -2

The properties of equality allow us to manipulate equations in order to solve for a variable.

Properties of Equality

The properties of equality, also referred to as PoEs, describe how an equation can be changed while remaining true. There are numerous PoEs such as the reflexive, substitution, and addition properties of equality. However, for the purposes of this question, the most important is the division property of equality. The division property of equality states that if both sides of an equation are divided by the same number, the equation is still true. In other terms:

Solving for a Variable

To find an unknown variable, we need to isolate the variable. This means using the properties of equality and other techniques to get the variable all by itself on one side of the equation. To isolate j, we need to divide both sides of the equation by -2. This will isolate j and maintain equality as shown by the division property of equality.

By dividing both sides by -2, we can see that j = -15/2.

Pepe Rodriquez works 42.5 hours at $6.20 per hour. The first 40 hours would be paid at the standard rate of $6.20 per hour, equaling $248.

The correct answer is B. $263.50, which is calculated by taking the standard pay of 40 hours at $6.20 per hour ($248) and adding the time-and-a-half pay of 2.5 hours at $9.30 per hour ($23.25).

Pepe Rodriquez works 42.5 hours at $6.20 per hour. The first 40 hours would be paid at the standard rate of $6.20 per hour, equaling $248. The remaining 2.5 hours would be paid at time-and-a-half, which is 1.5 times the hourly rate of $6.20, equaling $9.30 per hour. The total pay for the 2.5 hours is therefore $9.30 x 2.5 hours = $23.25. Adding the standard pay of $248 to the time-and-a-half pay of $23.25 yields a total of $263.50. Therefore, the correct answer is B. $263.50.

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the type of slope of the line is positive, as the coefficient of x (which is the slope) is positive. The y-intercept is -0.9, which means that the line intersects the y-axis at the point (0, -0.9).

The equation of the line y = 1.4x - 0.9 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Comparing the given equation with the slope-intercept form, we can see that the slope is 1.4 and the y-intercept is -0.9. Therefore, the type of slope of the line is positive, as the coefficient of x (which is the slope) is positive. The y-intercept is -0.9, which means that the line intersects the y-axis at the point (0, -0.9). The y-intercept, on the other hand, is the point where the line intersects the y-axis. In the equation y = mx + b, b is the y-intercept. In the case of the given equation, we can see that the y-intercept is -0.9. This means that the line intersects the y-axis at the point (0, -0.9). The slope and y-intercept are important characteristics of a line because they can be used to graph the line and to write its equation in slope-intercept form. In addition, they can be used to calculate the x-intercept, which is the point where the line intersects the x-axis, and to determine the equation of a parallel or perpendicular line.

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The probability that exactly 15 out of 20 adults use their smartphones in meetings or classes is approximately 0.0667, rounded to four decimal places as requested.

This is a binomial distribution problem where:

n = 20 (number of trials)

p = 0.57 (probability of success)

We want to find the probability that exactly 15 out of 20 adults use their smartphones in meetings or classes.

Using the binomial probability formula:

[tex]P(X = k) = (n choose k) * p^k * (1-p)^(n-k)[/tex]

where (n choose k) = n!/(k!(n-k)!)

[tex]P(X = 15) = (20 choose 15) * 0.57^15 * (1-0.57)^(20-15)[/tex]

[tex]P(X = 15) = (15504) * 0.57^15 * 0.43^5[/tex]

[tex]P(X = 15) ≈ 0.0667[/tex]

Therefore, the probability that exactly 15 out of 20 adults use their smartphones in meetings or classes is approximately 0.0667, rounded to four decimal places as requested.

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Assume that when adults with smartphones are randomly​selected, 57​% use them in meetings or classes. If 20 adult smartphone users are randomly​ selected, find the probability that exactly 15 of them use their smartphones in meetings or classes. The probability is _____? ​(Round to four decimal places as​ needed.)

Counter example:

3 - 7 = -4

5 - 8 = -3

8 -9 = -1

Conclusion: the difference between two positive numbers can also be a negative number.

What is meant by negative numbers?

Given are given a set of difference of positive numbers.

7 - 3 = 4

8 - 5 = 3

9 - 8 = 1

The conclusion for this difference is given as the difference between two positive numbers is always positive.

We are asked to give a counter example.

Now a counterexample means an example that makes the given conclusion invalid.

So the counterexample of given example would be to prove the difference between positive numbers can also be a negative number.

For example,

3 - 7 = -4

5 - 8 = -3

8 -9 = -1

Therefore using the same numbers but subtracting the larger numbers from smaller number, we proved that the difference between positive numbers can also be a negative number.

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