Sergio had $500.00 saved for a family trip. Six weeks later he had saved $860.00. At what rate of change did Sergio savings grow

The conversion of 28 inch to cm is 71.12 cm.

Kilometer (km) and mile are both units of distance or length, but they are used in different parts of the world.

A kilometer is a metric unit of length used in most countries outside the United States. It is defined as 1,000 meters, or approximately 0.62 miles.

To convert inches to centimeters, you can use the conversion factor of 1 inch = 2.54 centimeters.

So, to convert 28 inches to centimeters, you can multiply 28 by 2.54:

28 inches * 2.54 cm/inch = 71.12 cm

Therefore, 28 inches is approximately equal to 71.12 centimeters.

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The volume of the solid obtained by rotating the region bounded by the curves about the x-axis is π/77 (243 - 9sqrt(3)).

To find the volume of the solid obtained by rotating the region bounded by the curves about the x-axis, we can use the method of cylindrical shells. This involves integrating the circumference of a cylindrical shell times its height to obtain the volume of each shell, and then adding up the volumes of all the shells to get the total volume.

First, let's find the points of intersection of the two curves:

2/7 x^2 = 9/7 - x^2

9/7 = 9/7 x^2 + 2/7 x^2

9/7 = 11/7 x^2

x^2 = 9/11

x = ±sqrt(9/11)

The solid we obtain by rotating this region about the x-axis will have cylindrical shells with height dx, radius x, and circumference 2πx. Therefore, the volume of each shell will be:

dV = 2πx × h × dx

where h is the difference between the y-values of the curves at x:

h = (9/7 - x^2) - (2/7 x^2) = 9/7 - 9/7 x^2

Therefore, the total volume of the solid will be:

V = ∫(from x = -sqrt(9/11) to x = sqrt(9/11)) 2πx * (9/7 - 9/7 x^2) dx

V = 2π/7 ∫(from x = -sqrt(9/11) to x = sqrt(9/11)) x(9 - 9x^2) dx

We can simplify the integrand by setting u = 9x^2:

du/dx = 18x

dx = du/18x

Substituting:

V = 2π/7 ∫(from u = 9/11 to u = 81/11) (1/2)u^(1/2) (9/2) (du/18x)

V = π/7 ∫(from u = 9/11 to u = 81/11) u^(1/2) / x du

V = π/7 ∫(from u = 9/11 to u = 81/11) u^(1/2) / sqrt(9/11 - u/11) du

This integral can be evaluated using a trigonometric substitution. Let u = 9/11 sin^2 θ, then:

du/dθ = (18/11) sin θ cos θ dθ

Substituting:

V = π/7 ∫(from θ = π/6 to θ = π/2) (81/121) sin^3 θ dθ

V = π/7 [(81/121) * (3/4) - (9/121) × (sqrt(3)/2)]

V = π/77 (243 - 9sqrt(3))

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The integral of sec(x) is ln |sec(x) + tan(x)| + C.

The integral of sec(x) is:

∫sec(x) dx = ln |sec(x) + tan(x)| + C

where C is the constant of integration.

To solve this integral, you can use the method of substitution. Let u = sec(x) + tan(x). Then [tex]du/dx = sec(x)tan(x) + sec^2(x)[/tex], which can be simplified to du/dx = u tan(x). Rearranging, we get du/u = tan(x)dx.

Substituting these expressions into the integral, we have:

∫sec(x) dx = ∫(sec(x) + tan(x))/(sec(x) + tan(x)) dx = ∫(1/u) du

Integrating this expression gives:

∫(1/u) du = ln |u| + C = ln |sec(x) + tan(x)| + C

Therefore, the integral of sec(x) is ln |sec(x) + tan(x)| + C.

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The value of x in the quadrilateral is 8 .

The diagram above is a quadrilateral because it has fur sides. The opposite side of the diagram is equal to each other.

Therefore, let's establish the relationship base on the congruent sides.

The value of x can be found as follows:

5x + 6 = 7x - 10

subtract 7x from both sides of the equation

5x - 7x + 6 = 7x - 7x - 10

-2x + 6 = - 10

subtract 6 from both sides of the equations

-2x + 6 = - 10

-2x + 6 - 6 = - 10 - 6

-2x = -16

divide both sides by -2

-2x / -2 = -16 / -2

x = 8

Therefore,

x = 8

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Answer:

56.8 AND 33.2

Step-by-step explanation:

Complementary angles add up to 90 degrees, so we can set up the equation:

x + (x - 23.6) = 90

Simplifying the equation, we get:

2x - 23.6 = 90

Adding 23.6 to both sides, we get:

2x = 113.6

Dividing by 2, we get:

x = 56.8

So one angle measures 56.8 degrees, and its complementary angle measures:

90 - 56.8 = 33.2 degrees.

Answer:1 l = 2.2 lb wt.

Step-by-step explanation:

Answer: 15

Step-by-step explanation:

first you would subtract -69 by positive 420 to get 15

Answer:

i am sorry i am no se

peack englis

Answer:

1000 litros x 1000000 ml/litro = 1 000 000 000 mililitros

Answer:

86.1825503

Step-by-step explanation

190 pounds to kg is 86.1825503

The solutions to the equation f(x) = g(x) to the nearest hundredth are:  x = -8.85, -5.1 and x = 0.6

To find the solutions to the equation f(x) = g(x), we need to solve for x such that:

0.15x³ + 2x² + 7x - 3.3 = 1.5x - 7.3

We can simplify this equation by bringing all the terms to one side:

0.15x³ + 2x² + 5.5x - 4 = 0

To find the solutions to the nearest hundredth, we can use a graphing calculator or software to graph the functions f(x) and g(x) and find their points of intersection.

Using a graphing calculator , we can plot the two functions and find that they intersect at two points;

approximately x = -8.85, -5.1 and x = 0.6

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Thus, only 6.25 grammes of the initial 200 grammes of Co-60 will be present after 26.3 years.

Any time energy is moved, radiation is created. A substance does not need to be radioactive in order to emit radioactivity. Radiation is not always released by element compounds. Alpha particles, light, and heat are all instances of radiation.

To solve this problem, we can use the exponential decay formula:

N = N0 * (1/2)^(t/T)

where:

N is the amount of Co-60 remaining after a time t

N0 is the initial amount of Co-60

t is the time elapsed since the initial measurement

T is the half-life of Co-60

We are given N0 = 200 g, T = 5.26 years, and t = 26.3 years. We can plug in these values to get:

N = 200 * (1/2)^(26.3/5.26)

Simplifying the exponent, we get:

N = 200 * (1/2)⁵

Evaluating the exponent, we get:

N = 200 * 1/32

N = 6.25

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The correct question is:

the half-life of colbalt-60 (used in radiation therapy) is 5.26 years (actual data). How much a of 200 g sample of colbalt-60 will remain after 26.3 years?

George's average score is given as follows:

70.7%.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.

The seven observations for this problem are given as follows:

76, 58, 90, 44, 81, 73, 73.

The sum of these seven observations is of:

76 + 58 + 90 + 44 + 81 + 73 + 73 = 495.

Hence the mean, representing the average score, is obtained as follows:

495/7 = 70.7%.

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The given integral is solved by using integration by parts. And the required answer for the integral of x lnx is [tex]\int x\ln (x) \;dx=\frac{1}{2}x^2\ln x-\frac{1}{4}x^2+C[/tex].

Integration by parts is a special method that is used when we have to integrate the product of two functions. This method is also called the product rule for integration. Using this method, we consider the integral of x ln x as the product of two functions such as x and ln x. This is solved by using the formula, [tex]\int u\;dv = uv- \int v\;du[/tex].

Let's take u = ln x, dv = x dx, [tex]v=\frac{1}{2}x^2[/tex], [tex]du =\frac{1}{x}dx[/tex]. Then,

[tex]\begin{aligned}\int u\;dv &= uv- \int v\;du\\\int \ln x \cdot xdx&=\ln x\times \frac{x^2}{2}-\int \frac{x^2}{2}\times\frac{1}{x}dx\\&=\frac{1}{2}x^2\ln x-\frac{1}{2}\int xdx\\&=\frac{1}{2}x^2\ln x-\left[\frac{1}{2}\times\frac{1}{2}x^2\right]+C\\&=\frac{1}{2}x^2\ln x-\frac{1}{4}x^2+C\end{aligned}[/tex]

The required answer is [tex]\int x\ln (x) \;dx=\frac{1}{2}x^2\ln x-\frac{1}{4}x^2+C[/tex].

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Answer:

≈ 106.5 feet

Step-by-step explanation:

Let's start by drawing a picture of the situation. Imagine a kite flying in the air, with a string attached to it that is pulled taut (pulled tight so there's no slack). The string is 86 feet long. We want to know how high the kite is in the air, and we know that the angle of elevation of the kite is 53 degrees.

Now, the angle of elevation is the angle between the horizontal (the ground) and the line of sight from the observer (you) to the object (the kite). In this case, you are looking up at the kite, so the line of sight is the string that connects the kite to the ground.

To find the height of the kite, we need to use trigonometry. Specifically, we'll use the tangent function, which relates the opposite side of a right triangle (in this case, the height of the kite) to the adjacent side (in this case, the length of the string) and the angle of elevation.The formula for the tangent function is:

tan(theta) = opposite/adjacent

Where theta is the angle of elevation, opposite is the height of the kite, and adjacent is the length of the string.

We know that the angle of elevation is 53 degrees, and the length of the string is 86 feet. So we can plug those values into the formula and solve for the height of the kite:

tan(53) = opposite/86

opposite = 86 * tan(53)

         ≈ 106.5

So the height of the kite is approximately 106.5 feet.

The dolphin traveled a total vertical distance of 17 feet during its jump. Note that the negative sign for the second and third parts of the jump indicates that the dolphin was descending during those parts.

Distance is the total amount of space traveled by an object or a person, regardless of the direction taken. It is a scalar quantity and is usually measured in units such as meters (m), kilometers (km), feet (ft), or miles (mi). Distance is different from displacement, which is the shortest distance between the starting and ending points in a particular direction.

The total vertical distance the dolphin traveled is the sum of the distances it traveled during each part of the jump:

Distance traveled during the first part of the jump (underwater to the surface): 27 feet - (-35 feet) = 62 feet

Distance traveled during the second part of the jump (out of the water to the surface): 0 feet - 27 feet = -27 feet

Distance traveled during the third part of the jump (surface to underwater): -18 feet - 0 feet = -18 feet

Total vertical distance traveled: 62 feet + (-27 feet) + (-18 feet) = 17 feet

Therefore, the dolphin traveled a total vertical distance of 17 feet during its jump. Note that the negative sign for the second and third parts of the jump indicates that the dolphin was descending during those parts.

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Let's represent the area of the lawn with "x" (in square meters).

Maria charged $135 plus $9.55 per square meter, so her total earnings can be expressed as:

Total earnings = $135 + $9.55 x

We know that Maria was paid $1854, so we can set up an equation and solve for x:

$1854 = $135 + $9.55 x

Subtracting $135 from both sides:

$1719 = $9.55 x

Dividing both sides by $9.55:

x = 180

Therefore, the area of the lawn is 180 square meters.

An 8-sided polygon is called an octagon. The word "octagon" comes from the Greek words "okto," which means "eight," and "gonia," which means "angle."

An octagon is a two-dimensional shape that has eight straight sides and eight angles. All of the angles in an octagon add up to 1080 degrees, and each of the eight angles in a regular octagon (an octagon with equal side lengths and equal angles) measures 135 degrees.

Octagons are a common shape in geometry and can be found in a variety of applications, such as in architecture, art, and engineering. For example, many stop signs and traffic signals are octagonal in shape. In architecture, octagons are used in the design of buildings and rooms, and are often used to create interesting visual effects.

In summary, an 8-sided polygon is called an octagon, which is a two-dimensional shape with eight straight sides and eight angles.

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Answer:

172.72 cm

Step-by-step explanation:

5 feet 8 inches in cm = [(5×12)+8] x 2.54 = 68 x 2.54 = 172.72 cm

Answer:

3x13=39

Step-by-step explanation:

ellie=13

kid 1=13

kid 2 =13

The area of the trapezoidal cross section of the dam when the height is 180 feet is 33,030 square feet.

A quadrilateral is a four-sided polygon, having four edges and four corners.

Let's h be the height of the trapezoid.

The length of the bottom base is 2 times "h", or 2h.

The length of the top base is 1/5 times "h", or h/5, minus 30 feet, which we can write as (h/5) - 30.

Area of a trapezoid = (1/2) × (length of bottom base + length of top base) × height.

The expression for the area of the trapezoidal cross section of the dam is:

(1/2) × (2h + (h/5 - 30)) × h

If the height of the dam is 180 feet, we can plug that value into the expression we just wrote to find the area:

Area = (1/2) × (2(180) + ((180/5) - 30)) × 180

Area = (1/2) × (360 + (36 - 30)) × 180

Area = (1/2) × (360 + 6) × 180

Area = (1/2) × 366 × 180

Area = 33,030 square feet

Therefore, the area of the trapezoidal cross section of the dam when the height is 180 feet is 33,030 square feet.

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Answer:

aabc

Step-by-step explanation:

Data can be divided on the basis of qualitative nature into two types as follows:

Thus, it is clear that nominal data can not be ranked or ordered but ordinal data are the type of qualitative data that are categorised and then ranked or ordered.

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Answer: the amount of polonium remaining in the sample 1104 days later is approximately 0.12 g, and the answer is C

Step-by-step explanation:

To determine how many half-lives of polonium-210 occur in 1104 days, we can divide 1104 by the half-life of 138 days:

1104 / 138 ≈ 8

Therefore, there are approximately 8 half-lives of polonium-210 in 1104 days.

To determine how much polonium is in the sample 1104 days later, we can use the fact that the amount of polonium remaining after n half-lives is given by:

Amount remaining = initial amount × (1/2)^n

where n is the number of half-lives that have occurred.

In this case, we know the initial amount is 30 g and the number of half-lives is 8. So we can calculate the amount of polonium remaining as:

Amount remaining = 30 g × (1/2)^8 ≈ 0.117 g ≈ 0.12 g (rounded to two decimal places)

Therefore, the amount of polonium remaining in the sample 1104 days later is approximately 0.12 g, and the answer is C.

The required value table is  

x    -1     0     1      2    3

y    -3    1      5     9    13

To find the value table of a linear function take, any values for 'x' and from that find the 'y' values for each corresponding value of 'x'.

Here in this problem, we are taking x values as 0, 1, 2, and 3. Now substitute each of the 'x' values and find the 'y' values and make the table of values.

Here we have  

The linear function given is y = 4x + 1

To find the value table we are taking x values as - 1, 0, 1, 2, 3  

At x = - 1 => y = 4(-1)  + 1

=> y = - 4 + 1

=> y = - 3

At x = 0 => y = 4(0) + 1

=> y = 0 + 1

=> y = 1

At x = 1 => y = 4(1) + 1

=> y = 4 + 1

=> y = 5

At x = 2 => y = 4(2) + 1

=> y = 8 + 1

=> y = 9

At x = 3 => y = 4(3) + 1

=> y = 12 + 1

=> y = 13

Therefore,

The required value table is  

x    -1     0     1      2    3

y    -3    1      5     9    13

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Using trigonometric identity, cos(2θ-1) / cos(2θ+1) is equal to [(1 - 2tan^2(θ))cos(1) + 2tan(θ)sin(1)] / [(1 - 2tan^2(θ))cos(1) - 2tan(θ)sin(1)]

We can use the trigonometric identity:

cos(2θ) = 1 - 2sin^2(θ)

to rewrite the expression as follows:

cos(2θ-1) = cos(2θ)cos(1) + sin(2θ)sin(1) = (1 - 2sin^2(θ))cos(1) + 2sin(θ)cos(θ)sin(1)

Similarly,

cos(2θ+1) = cos(2θ)cos(1) - sin(2θ)sin(1) = (1 - 2sin^2(θ))cos(1) -  2sin(θ)cos(θ)sin(1)

Dividing these two expressions, we get:

cos(2θ-1) / cos(2θ+1) = [(1 - 2sin^2(θ))cos(1) + 2sin(θ)cos(θ)sin(1)] / [(1 - 2sin^2(θ))cos(1) - 2sin(θ)cos(θ)sin(1)]

Now, we can use the identity:

tan(θ) = sin(θ) / cos(θ)

to simplify the expression. Specifically, we can express sin(θ) in terms of tan(θ) and cos(θ) as follows:

sin(θ) = tan(θ)cos(θ)

Substituting this into the expression for cos(2θ-1) / cos(2θ+1), we get:

cos(2θ-1) / cos(2θ+1) = [(1 - 2tan^2(θ))cos(1) + 2tan(θ)sin(1)] / [(1 - 2tan^2(θ))cos(1) - 2tan(θ)sin(1)]

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The measure of angle A to the neasrest degree is 46°.

Th figure in the image is a right triangle.

To solve for angle A, we use trigonometric ratio

Cosine = adjacent / hypotenuse

Plug in the values and solve for A.

cosA = 7.8/11.2

Take the cos inverse

A = cos⁻¹( 7.8/11.2 )

A = 46°

Therefore, angle A is 46 degrees.

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In the case of converting 3cm to mm, we find that there are 30mm in 3cm.

Understanding how to convert measurements is a fundamental skill that will serve you well in many areas of study. In this case, we'll focus on how to convert 3cm to mm.

First, it's important to understand that cm and mm are both units of measurement for length or distance. The abbreviation cm stands for centimeters, while mm stands for millimeters. A centimeter is larger than a millimeter, with 1cm equaling 10mm.

To convert 3cm to mm, we need to use this relationship between the two units of measurement. We know that 1cm is equal to 10mm, so we can use multiplication to find out how many millimeters are in 3cm.

We can start by writing out the equation:

3cm x 10mm/1cm

In this equation, we're multiplying 3cm by the conversion factor of 10mm/1cm. This conversion factor tells us that there are 10mm in 1cm. When we multiply 3cm by this conversion factor, we get:

3cm x 10mm/1cm = 30mm

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The equivalent value of 5 ft 7 in cm is 170.18 centimeters

In today's world, measurements play a crucial role in almost everything we do. Whether it's measuring ingredients for a recipe or calculating distances for a road trip, we rely on accurate measurements to ensure success. And as we live in a globalized world, it's important to be able to convert measurements from one unit to another. In this article, we will discuss how to convert the height of 5 feet 7 inches into centimeters.

To convert 5 feet 7 inches into centimeters, we need to first understand the conversion factor between feet and centimeters. 1 foot is equal to 30.48 centimeters. Therefore, to convert 5 feet into centimeters, we can multiply 5 by 30.48, which gives us 152.4 centimeters.

Now, we need to convert the 7 inches into centimeters. 1 inch is equal to 2.54 centimeters.

To convert 7 inches into centimeters, we can multiply 7 by 2.54, which gives us 17.78 centimeters.

Finally, to get the total height in centimeters, we can add the two values we obtained in the previous steps. Therefore, the height of 5 feet 7 inches is equal to

=> (152.4 + 17.78) = 170.18 centimeters

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Answer:

3/4

Step-by-step explanation:

Answer:

The slope is [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

We are given two points (2,5) and (-2,2). If we need to find the slope, there are two methods which we can use to find the slope.

Method 1: Count the slope

We can use [tex]\frac{rise}{run}[/tex] to count the slope.

Counting the slope, we get [tex]\frac{3}{4}[/tex] which cannot be simplified.

Method 2: Slope formula

We can use the formula [tex]\frac{y2-y1}{x2-x1}[/tex] to find the slope as well.

We just have to plug in our coordinates into the formula to get the answer.

[tex]\frac{2-5}{-2-2}[/tex]

Evaluate

[tex]\frac{-3}{-4}=\frac{3}{4}[/tex]

Limiting reagent calculator provides you the most reliable results in a fraction of seconds without any error that arises in the manual calculation.

A limiting reactant calculator online is a tool used to calculate the amount of reactant needed to produce a specific product. The calculator helps you determine the limiting reactant in a chemical reaction, which is the reactant that will be completely consumed in the reaction.

It does this by calculating the amount of reactant needed to produce the desired amount of product. Once the limiting reactant is known, the amount of excess reactant can be determined.

This calculator can be used to optimize chemical reactions, helping to maximize the amount of product produced while minimizing the amount of reactants used. This can help reduce costs and material waste.

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