A person places $103 in an investment account earning an annual rate of 1.9%, compounded continuously. Using the formula V = P e r t V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 6 years.

The area of the trapezium shown is 284.31 in²

An equation is an expression that shows the relationship between variables and numbers.

The area is calculated for a two dimensional shape. It shows the amount of space occupied for that shape.

The area of a trapezium is given by:

Area = (1/2)(sum of parallel sides) * height

For the trapezium shown, the parallel sides have a measure of 17 inches and 31 inches respectively. The height is 11.7 inches, hence:

Area = (1/2)(17 + 31.6)(11.7) = 284.31 in²

The area is 284.31 in²

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Answer:

In algebra, the 3x + 1 semigroup is a special subsemigroup of the multiplicative semigroup of all positive rational numbers. The elements of a generating set of this semigroup are related to the sequence of numbers involved in the still open Collatz conjecture or the "3x + 1 problem".

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

[tex]\frac{8+x}{24+x}=\frac{3}{5}\\ \\ 5(8+x)=3(24+x)\\\\40+5x=72+3x\\\\5x=32+3x\\\\2x=32\\\\x=16[/tex]

Answer:

His secret is in generalizing two roots together instead of keeping them as separate values.

Mark brainiest

The amount of money, to the nearest cent, in the account after 10 years is found as $742.87.

The formula for the continuous compound  is:

V = Pe^{rt}

In which:

V= 358*2.72*{0.073*10}

V = 358*2.07

V = 742.87

Thus, the amount of money, to the nearest cent, in the account after 10 years is found as $742.87.

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In designing the waterskiing ramp using direct variation the vertical supports, y will be related to the horizontal distance, x by a constant k,  as in the relation

k = y/x

The ratio between two quantities that are directly proportional is the constant of proportionality.

When two quantities grow and shrink at the same rate, they are directly proportional.

When y and x are two values that are directly proportional to one another, the proportionality constant k is defined as k=y/x.

In the problem, the distances between the vertical supports is x while the height of the support is y. To have a direct proportionality this relationship between x and y must be a constant say k.

Hence we say k = y / x

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The price of a new video game, before tax in the shop that London visited is $10.00

The question is a percentage problem, percent is a fraction of hundred and the calculations will be using 100

In the store that London visited, they were offering a 20% discount

= 20 percent

= 20 / 100

= 0.2

discount factor = 1 - 0.2 = 0.8

the discount factor will be used to multiply by the price of the video game to get a new price

selling price of the new video game before tax = $50 * 0.2 = $10

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The first number in an ordered pair (x,y) is the x-coordinate, also called the "abscissa". It represents the horizontal position of the point on a coordinate plane. The second number in an ordered pair is the y-coordinate, also called the "ordinate". It represents the vertical position of the point on a coordinate plane.

5.1 inches is the correct answer. o.o :P C: 0'0 your welcome sir/ma'am also i dont want this deleted because i did the work for this so pls dont delete it ok? plssssss donttttt deleteeeeeee ittttttt plssssss dont deleteeee iitttt ty c;

If the original shape is scaled by a factor of 2, the resultant shape is twice as large as the original shape.

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If the original shape is scaled by a factor of 2, the resultant shape is twice as large as the original shape.

The scale factor is calculated using the following fundamental formula: Scale factor = Dimension of the new shape Dimension of the old shape. The formula for calculating the scale factor is expressed as Scale factor = Larger figure dimensions Smaller figure dimensions in the event that the original figure is magnified.

Consider being told that the smaller square's side length is 2 inches and that the ratio of the smaller to the larger square is 1: 2. So, 1 inch on the smaller square is equivalent to 2 inches on the larger square, just in case you forgot. A lesser value will result from multiplying by the scale factor, which is 1/2. A number having more than two elements is referred to as a prime number if it has no more than two factors.

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There are 1.449 ×  10⁸ pet fish and pet reptiles all together in the United States.

Total number of pet fish in the United states = 1.4 ×  10⁸

Total number of pet reptiles in the United States = 4.9 × 10⁶

So the total number of pet fish and pet reptiles = (1.4 ×  10⁸) + (4.9 × 10⁶)

= 1.449 ×  10⁸

The final answer is in scientific notation. Scientific notation is the way of writing number that are too big or too small and inconvenient to write in decimal form. They are expressed in the multiple of 10 with a suitable power on 10.

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Answer: 28x^4y^7

Step-by-step explanation: Add exponents of common base

Answer:

28x⁴y⁷

Step-by-step explanation:

First multiply the numbers;

Then combine the exponents;

Then combine the exponents again;

Then you have the answer :)

The magic ratio for muffins in 2:2:1:1.

The magic muffin ratio is 2:2:1:1. This equates to 2 parts flour, 2 parts liquid, 1 part fat, and 1 part eggs. The most crucial aspect is to remember to utilize the same unit of weight for each component!

Rinse frozen blueberries many times in cold water until the water turns lighter in color to prevent your batter and baked items from developing a purple-blue tint. Then, blot them dry with a paper towel and gently fold them into the batter. The goal of this procedure is to maintain fast breads light and delicate by limiting the quantity of gluten produced during the mixing process. To do this, the dry components are mixed in a one bowl, the wet ingredients are combined in a separate bowl, and then the two mixtures are combined together.

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The image of (12,-12) after a dilation by a scale factor of 1/3 centered at the origin is (4, -4).

What is dilation at origin?

On the coordinate plane, figures can be magnified. The centre of dilation is frequently the origin. The coordinates of the points in the preimage can be multiplied by the scale factor to get the points in the image if you are distorting a figure that is centered at the origin.

We have to find the image of (12,-12) after a dilation by a scale factor of 1/3 centered at the origin.

To find the image after dilation multiply both coordinates (12, -12) by 1/3 which is the same as dividing by 3.

⇒  (12, -12)*1/3 = (4, -4)

Hence, the image of (12,-12) after a dilation by a scale factor of 1/3 centered at the origin is (4, -4).

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The y-intercept of the graph of f(x) = x^2 - 3x + 5 is (0, 5).

The equation of the axis of symmetry is x = (3/2).

The x-coordinate of the vertex is (3/2), and the y-coordinate of the vertex is (5 - (9/4)) = (-1/4).

So the vertex of the graph of f(x) = x^2 - 3x + 5 is (-1/4, (3/2)).

To graph the function, you can start by plotting the vertex, then use the axis of symmetry to reflect the parabola across the line x = (3/2). The y-intercept is the highest point of the parabola if it opens upwards, and the lowest if opens downwards. This can be used to confirm the direction of the parabola.

A quadratic function's U-shaped curve is seen on a parabola graph. A right circular cone and a plane surface intersect to generate one of the conic sections known as a parabola in mathematics. It has a U-shaped symmetry in the plane. The conventional form of a parabola is a graph whose equation takes the form f(x) = ax2+bx+c. A parabola's vertex is its most extreme point, and the vertical line that runs through it forms its axis of symmetry.

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So on solving the provided question, we can say that inequality equation will be as follows r - 8 <= 7 r<=15 or r >= -15

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

here the question, is

r - 8 <= 7

r<=15

or r >= -15

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Due to the lack of spatial thinking instruction in most math classes, geometry is hard. They should acquire geometrical ideas easily instead.

The father of geometry, Euclid was a brilliant mathematician. The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.

The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.

Everyone finds it difficult to dive into the issue of proofs. Children must realize that this issue affects everyone, even the mathematically skilled. Because they have trouble seeing how 3D, and 2D, forms, angles, and lines connect from various viewpoints, most youngsters struggle with geometry issues. Even kids who are really good at solving sum problems in math might be utterly stumped by this.

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Due to the lack of spatial thinking instruction in most math classes, geometry is hard. They should acquire geometrical ideas easily instead.

Visual Ability: While some kids think in terms of forms and proportions, others think visually. Children must comprehend geometry in order to visualize, or else they may not be able to see things in a larger context.

Numbers & Measurements: Children will learn about the link between shapes and sizes as numbers and measures come to life in shapes and sizes. Children will be able to comprehend the measurements and connections of lines, angles, surfaces, and solids using numbers and measures.

3D Thinking: Since these ideas originated in geometry, children cannot possibly comprehend 2 and 3 dimensions without having a working knowledge of geometry! The only way to visualize X, Y, and Z axis, triangles, and pyramids are with the aid of geometry.

Spatial Understanding: If it weren't for geometry, kids could have trouble comprehending the notion of spatial comprehension. Children will learn to appreciate the wonders of the world by studying concepts relating to space, location, size, and shape of objects.

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The correct choice is:

y= x^2 and y= 2x+3

Given equation,

x^2=2x+3

this can be used for factorization by taking all the factors in one side of the equation

x^2-2x-3=0

or, x^2-3x+x-3=0

or, x(x-3)+x(x-1)=0

or, (x-3)(x-1)=0

Therefore,

x=-1 or x= 3

The result indicates,

when we plot the equation x^2=2x+3 in graph, as a function of y=x^2-3x+x-3, the x axis will be intersected on x=-1 and x=3

Now, if we consider

y=2x+3 and y=x^2

it gives  x^2-2x-3=0 all over again, when combined.

The solution to,

x^2=2x+3 is the intersection point of the graph of straight line alongside the graph for the quadratic equation curve.

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The correct answer is y= [tex]x^{2}[/tex] and y= 2x+3 that can be graphed to find the solution(s) to [tex]x^{2}[/tex]= 2x + 3 .

The Given equation was ,

[tex]x^{2}[/tex]= 2x + 3 .

this can be used for factorization by taking all the factors in one side of the equation

[tex]x^{2}[/tex] - 2x - 3 =0

or, [tex]x^{2}[/tex]-3x+x-3=0

x(x-3)+x(x-1)=0

(x-3)(x-1)=0

∴x=-1 or x= 3

The result indicates,

when we plot the equation [tex]x^{2}[/tex]=2x+3 in graph, as a function of y=[tex]x^{2}[/tex]-3x+x-3, the x axis will be intersected on x=-1 and x=3

Now, if we consider

y=2x+3 and y=x^2

it gives  [tex]x^{2}[/tex]-2x-3=0 all over again, when combined.

The solution to,

[tex]x^{2}[/tex]=2x+3 is the intersection point of the graph of straight line alongside the graph for the quadratic equation curve.

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The partial fraction expansion for the rational function

S/ (s - 7) (s^2 - 49) = -25-56/ (5+3) (s^2+ 16) - 2s - 56 / (s +3) (s^2 + 16)

can be found by decomposing it into the sum of simpler fractions.

One way to do this is to use the method of long division and then match the coefficients of the resulting polynomials. The process is as follows:

Divide S by (s - 7) to get a quotient of S1 and a remainder of R1.

Divide R1 by (s^2 - 49) to get a quotient of S2 and a remainder of R2.

Write the expansion as S1 + S2 + R2/(s - 7)(s^2 - 49)

Alternatively, we can use the method of partial fraction decomposition by inspection.

To do this, you will write the rational function as the sum of simpler fractions with the same denominator.

S/ (s - 7) (s^2 - 49) = A/(s-7) + B/ (s^2 - 49) + (C*s + D)/(s^2 - 49)

where A, B, C, and D are unknowns that you will find by matching coefficients.

S = (A(s^2-49) + B(s-7) + C*s + D) / (s-7) (s^2-49)

You can use this equation to solve for A, B, C, and D by matching coefficients.

-25-56/ (5+3) (s^2+ 16) - 2s - 56 / (s +3) (s^2 + 16) = A/(s-7) + B/(s^2 - 49) + (C*s + D)/ (s^2 - 49)

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Answer:

Step-by-step explanation:

s = # of small boxes

l = # of large boxes

s + l = 10

10s + 24l = 184

Answer: if one hiker walks faster than the other, their rate would be 9.68mph or 9.7mph if u round up and the rate of the other hiker that is walking slower is 4.4mph.

Step-by-step explanation:

For the hiker walking 2.2mph

I did: 22 x 2.2 = 48.4/5 = 9.68

Rate = 9.68mph

For the other hiker

I did: 22/5= 4.4

rate = 4.4mph

The average deviation of predicted DVD sales from the actual is 12.2279 million dollars. F-critical value is 4.0785>4.0785 we can reject the null hypothesis. The 95% confidence interval is (17.1536, 25.1554). The 95% prediction interval for the given value of x is (-3.8623, 46.1713).

Estimate the level of DVD sales for movies, by using the amount of annual revenue  generated by the box office gross

We randomly selected a sample of 43 movies for the same year.

Excel  α = 0.05,  r^2 = 0.5123

=51.23%

51.23% of the DVD sales variation is explained by annual revenue.

SY.X = 12.2279.

Therefore, the average deviation of predicted DVD sales from the actual is 12.2279 million dollars.

b. The hypothesis being tested is:

Null Hypothesis, H0: β1 = 0

Alternative Hypothesis, H1: β1 ≠ 0

The test statistic, F = (6439.6133/1)/((12570.025 - 6439.6133)/(42 - 1)) = 43.07

The F-critical value is 4.0785.

Since 43.07 > 4.0785, we can reject the null hypothesis.

Therefore, we can conclude that there is a linear relationship between the revenues of DVD sales and the box-office gross.

c. y = bo + b1*x

y = 4.8445 + 0.1631*x

Put x = 100

y = 4.8445 + 0.1631*100 = 21.1545

The 95% confidence interval for the given value of x is:

= y ± t*s*[tex]\sqrt{0.026249}[/tex]

= 21.1545 ± 2.020*12.2279*[tex]\sqrt{0.026249}[/tex]

= (17.1536, 25.1554)

d.  The 95% prediction interval for the given value of x is:

= y ± t×s×[tex]\sqrt{}[/tex]1 + hin [The t-value is calculated using =TINV(0.05,42-1) in Excel]

= 21.1545 ± 2.020*12.2279*[tex]\sqrt{1 + 0.026249}[/tex]

= (-3.8623, 46.1713)

Therefore, the value is (-3.8623, 46.1713).

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Answer:

39°

Step-by-step explanation:

[tex]angle \: 1 + 2 = 180(co \: interior \: angles \: \:in \: parallel \: lies \: are \: add \: up \: t \: equal \: 180) \\ [/tex]

13x + 24 + 5x -6 = 180

18x+ 18 =180

18x +18 -18 =180-18

18x = 162

18 18

x = 9

Therefore,

m<2 = 5x- 6

= 5(9) -6

= 45-6

= 39°

The solution to the following linear equation problem can be seen in the graph showing how the width and diameter of one face are linearly related.

In a linear model, one level is the maximum amount of levels that may be used. Any equation that has a theoretical extension of at least two is said to be nonlinear. There is a straight line on a map with a simple equation. A nonlinear equation's curve is depicted on the graph.

Here,

one face's perimeter and side lengths are linearly related.

line-drawing formula.

The formula y = mx + b can be used to describe a regular model.

If m is the rising rate and b is in reality the y intercept, then x and y are variables.

The graph shows a linear relationship between the length and perimeter of one face.

Therefore, the graph showing how the perimeter or edge length of one face are linearly connected is the solution to the provided linear equation problem.

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Answer:

all i could do was simplify it

Step-by-step explanation:

The number of cups of sugar that you will need to make lemonade would be = 2 cups of sugar.

A recipe is defined as the list of condiments that are used for the preparation of a food and it's guidelines.

In the recipe to make lemonade,

6 cups of water = 1/2 cup of sugar

24 cups of water = X cup of sugar.

Make X the subject of formula;

X cup of sugar = 24 × 1/2 ÷ 6

= 12/6 = 2 cups of sugar.

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Answer: To find Janice's running speed, we need to determine how many miles she runs per hour.

We know that the track is 1/4 mile long and Janice can complete each lap in 1/10 of an hour. To find the total number of miles Janice runs in an hour, we can multiply the length of the track by the number of laps she completes in an hour.

Length of the track * number of laps = total miles

1/4 mile * (1/10 hour)^-1 = total miles

On the second equation, we are using the inverse of the time, to get the number of laps completed in an hour

The speed is distance over time, so we need to express the distance in miles and the time in hours.

So Janice's running speed is 4 miles/hour.

Step-by-step explanation:

Pixel value refers to the numerical value assigned to a single pixel in an image.

It is usually a measure of the brightness of the pixel, with higher numbers indicating brighter pixels and lower numbers indicating darker pixels.

The range of values can vary depending on the image type, but typically, 8-bit images use a range of 0 (black) to 255 (white). Pixel values are used for a variety of tasks in digital image processing, such as analyzing the colors of an image or isolating objects in a scene.

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'Therefore , the solution of the given problem of function comes out to be  f⁻¹(x) =  1 + x / 5x+2 .

Mathematics is the study of number, their variations, the geographical tissue, architecture, and both both actual and fictitious locations. A equation  is a depiction of the relationship here between number of inputs and the corresponding outputs for each one. A function is just a collection of input that, when put together, provide one variable distinct output with each input. Every function is assigned a city, county, or scope, sometimes known as a realm.

Here,

Given:

=> f(x) = (1 -2x)/(5x-1)

To find f⁻¹(x)

So,

=> y = (1 -2x)/(5x-1)

=>  x =  (1 -2y)/(5y-1)

=> y = 1 + x / 5x+2

=> f⁻¹(x) =  1 + x / 5x+2

Therefore , the solution of the given problem of function comes out to be  f⁻¹(x) =  1 + x / 5x+2 .

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