Suppose an object moves along the y axis so that its location is yequals​f(x)equalsxsquaredplusx at time x​ (y is in​ meters, x is in​ seconds). Find ​(A) The average velocity​ (the average rate of change of y with respect to​ x) for x changing from 2 to 5. ​(B) The average velocity for x changing from 2 to 2+h. ​(C) The instantaneous velocity at xequals2 second. ​(A) The average velocity is 8 ​m/sec. ​(B) The average velocity is (nothing )​m/sec. ​(C) The instantaneous velocity is 5 ​m/sec.

If x and y vary inversely, we can write their relationship then the function that models the inverse variation is y = 80/x.

What is Function?

In mathematics, a function is a rule or mapping that associates each input value (also called the independent variable) with a unique output value (also called the dependent variable). Functions are often represented using an equation, formula, or a graph, and are used to model real-world phenomena and solve problems in various fields such as science, engineering, economics, and more.

They can take different forms and have different properties, such as being linear, quadratic, exponential, periodic, or more complex. Some common notation used to represent functions includes f(x), y = f(x), or simply y.

If x and y vary inversely, we can write their relationship as:

x * y = k

where k is a constant of proportionality. We can use the given initial values of x and y to solve for k:

10 * 8 = k

k = 80

Therefore, the function that models the inverse variation is:

x * y = 80

or

y = 80/x

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Answer:

$416.67

Step-by-step explanation:

8% = 0.08

adding 8% to something means you add 0.08 of it

original = 100% = 1

original + 8% increase = 1 + 0.08 = 1.08

1.08 of original price = new price = 450

1.08 * original price = 450

450/1.08 = original price = $416.67

The inequality that determines the maximum number of people that can go to the park is given as follows:

5.75 + 29.75x ≤ 210.

The costs associated with going to the park are given as follows:

Hence the total cost for x people going to the park is given by the following equation:

C(x) = 5.75 + 29.75x.

They can spend at most $210, hence the inequality that determines the maximum number of people that can go to the park is given as follows:

C(x) ≤ 210

5.75 + 29.75x ≤ 210.

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a) The standard deviation of  1.45 mpg.

b)The margin of error for the mean estimate 3.03 mpg

c) A 95% confidence interval for μμ is (28.1 - 3.03, 28.1 + 3.03) or (25.07, 31.13) mpg, the mean highway mpg for this vehicle is  27 mpg.

a) Using the formula for the standard error of the mean, σx¯ = σ/√n, where σ is the standard deviation of the population, n is the sample size, we can calculate σx¯ = 6.5/√20 ≈ 1.45 mpg.

b) Using a 95% confidence level, we can find the critical value for the t-distribution with 19 degrees of freedom (n-1), which is 2.093. The margin of error for the mean estimate is then t*σx¯ = 2.093 x 1.45 ≈ 3.03 mpg.

c) The 95% confidence interval for μ is given by x¯ ± margin of error, which is (28.1 - 3.03, 28.1 + 3.03) or (25.07, 31.13) mpg. Since the vehicle sticker information states a highway average of 27 mpg, the results of this experiment are not consistent with the vehicle sticker, as the 95% confidence interval does not contain the value of 27 mpg. This suggests that the vehicle may not be performing as well as expected, or that the sample of mpg readings was not representative of the overall population.

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The mathematical Expression is 5x- 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

Given:

We have the unknown variable x.

4 is subtracted from the product of 5 and a number.

Now, Translating the word problem (sentence) into an algebraic expression, we get

= 5x - 4

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The area of the parallelogram that is shown above would be = 9 yd².

A parallelogram is defined as the quadrilateral that has four sides whose sides are also parallel to each other.

The formula that can be used to calculate the area of the parallelogram = base × height ( diagonal)

The base = 4½ yd

height = 2 yd (diagonal)

Area = 4½× 2 = 9yd².

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Answer:

60

Step-by-step explanation:

10,000 * 2 = 20,000, so multiply 30 by 2:

30 * 2 = 60

Answer:

A 60 square meter pond is needed to accommodate 20,000 catfish.

Step-by-step explanation:

We know that 30 square meters is needed per 10,000 catfish.

How large a pond is needed for 20,000 catfish?

We can create an equation like this

[tex]\frac{30}{10000} =\frac{x}{20000}[/tex]

let [tex]x[/tex] represent the number of square meters needed for 20,000 catfish

Lets solve for [tex]x[/tex].

Cross multiply.

[tex]30*20000=x*10000[/tex]

Evaluate [tex]30*20000[/tex]

[tex]600000=10000x[/tex]

Divide both sides by [tex]10000[/tex].

[tex]60=x[/tex]

In a cas e whereby a fruit cocktail, for every 20 ml of orange juice you need 45 ml of apple juice and 100 ml of coconut milk the ratio of apple juice to coconut milk to orange juice expressed in its simplest form is 9: 20 : 4

The concept that will be used here is ratio.

The amount of orange juice can be expressed as  20mL

The amount of apple juice can be expressed as  45mL

The amount of coconut milk can be expressed as  100 mL

Then the ratio of the three can be expressed as :

(apple: coconut: orange)

= 45: 100 : 20

We can divide through by 5, then we have

9: 20 : 4

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The expression when simplified is 2c^3d^3(4cd^2 + 1)

From the question, we have the following parameters that can be used in our computation:

8c^4d^5+2c^3d^3

Factor out 2 from the expression

So, we have the following representation

2(4c^4d^5 + c^3d^3)

Factor out c^3d^3 from the expression

So, we have the following representation

2c^3d^3(4cd^2 + 1)

Hence, the expression is 2c^3d^3(4cd^2 + 1)

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The coordinates of D' will be at (x, - y) when reflected along the line Y-X.

Mathematical transformations can be used to move two-dimensional figures along a plane or coordinate system.

Dilation, To construct the image, the preimage is scaled up or down.

The image is a preimage that has been turned around or a reflection.

Rotation, To produce the final image, the preimage is rotated about a specified point.

Translation, The picture is relocated a set distance from the preimage while also being translated.

Given, A quadrilateral ABCD and one is the vertex D(x, y).

Now, The reflection of the quadrilateral ABCD is reflected across the Y-X.

We know a reflection along Y-X changes (x, y) to (x, -y).

Therefore, The vertex D' will have coordinates (x, - y).

Q. What are the coordinates of D'when the quadrilateral ABCDis reflected across the line Y - X, Given, preimage D(x, y).

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The value of x at the point of intersection is given as follows:

x = -1.

We must test for both definitions of the second function, and find which solution is in the correct range.

For the first definition, the solution is given as follows:

2x + 1 = x

2x - x = -1

x = -1.

-1 is less than 1, hence x = -1 is one solution to the system of equations.

For the second definition, the solution is given as follows:

2x + 1 = -x + 2

3x = 1.

x = 1/3.

Which is less than one, while the function is defined for values greater than 1, hence it is an extraneous solution.

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Answer:

6.28375

Step-by-step explanation:

times the radius will fit = x

8 * x = 50.27

x= 50.27÷8

x=6.28375

Answer:

XY = 18

Step-by-step explanation:

In this picture, XD = DW, and YE = EZ, so we are able to use the midline theorem. From the midline theorem, we can easily determine that (XY + WZ)/2 = DE. From this, we can plug in: (XY + [tex]\frac{4}{3}[/tex]XY) = 2 * 21. So, simplifying that equation gets: [tex]\frac{7}{3}[/tex]XY = 42. So, XY = [tex]42 * \frac{3}{7} = 18[/tex].

(if i'm going to be honest, i'm sure your geometry teacher covered this in class. just make sure to pay attention next time.)

Answer:

XY = 18 ft.

Step-by-step explanation:

Answer:

0.4850 knots.

Step-by-step explanation:

To convert the speed of the California Current from centimeters per second to knots, we can use the conversion factor of 1 knot = 0.514444444 cm/s.

So, 0.25 cm/s * 1 knot / 0.514444444 cm/s = 0.4850 knots.

Therefore, the California Current moves at a speed of approximately 0.4850 knots.

x = 415.

Check attached image 1.

So at this point, we know the measures of the angles, in terms of "x", which is a variable. We may use the implicit information in the drawing to find more information. Such as the total measure of the sum of angles DBE and CBE. This total measure equals 90°, we know this because there's a square drawn on the base of both angles. Whenever you see a square drawn at the base of an angle, it means the measure of that angle is 90°, a right angle.

Check attached image 2.

We know that the sum of angles DBE and CBE equal 90°. Hence:

[tex]DBE+CBE=90[/tex]

In terms of variable "x", this is:

[tex](0.1x-22)+(0.3x-54)=90[/tex]

[tex]0.1x-22+0.3x-54=90[/tex]

[tex]0.1x+0.3x-54-22=90\\ \\0.4x-76=90[/tex]

[tex]0.4x-76+76=90+76\\ \\0.4x=166[/tex]

[tex]\frac{0.4x}{0.4} =\frac{166}{0.4} \\ \\x=415[/tex]

To see if "x = 415" is the correct answer, take the original equation, substitute "x" by "415" and, if the same number appears on both sides of the equal (=) sign, then we've found our answer!

[tex](0.1x-22)+(0.3x-54)=90\\ \\(41.5-22)+(124.5-54)=90\\ \\(19.5)+(70.5)=90\\ \\90=90[/tex]

x = 415.

Answer:

Step-by-step explanation:

[tex]\mathrm{3x+5=5(x+3)}[/tex]

Expand:-

[tex]\mathrm{3x+5=5x+15}[/tex]

Subtract 5x from both sides:-

[tex]\mathrm{-2x+5=15}[/tex]

Subtract 5 from both sides:-

[tex]\mathrm{-2x=15-5}[/tex]

[tex]\mathrm{-2x=10}[/tex]

Divide both sides by -2:-

[tex]\mathrm{\cfrac{-2x}{-2}=\cfrac{10}{-2}}[/tex]

[tex]\mathrm{x=-5}[/tex]

___________________

Hope this helps!

The average rate of change of the function between x = a and x = a + h is -6

The slope is -6

From the question, we have the following parameters that can be used in our computation:

g(x) = -6x + 1

The interval is given as

x = a and x = a + h

So, we have

g(a) = -6a + 1

g(a + h) = -6(a + h) + 1

This gives

g(a) = -6a + 1

g(a + h) = -6a + -6h + 1

Subtract the functions

g(a) = -6a + 1

g(a + h) = -6a + -6h + 1

g(a) - g(a + h) = -6h

The average rate is then calcualated as

Average = [g(a) - g(a + h)]/(a - a - h)

This gives

Average = (-6h)/-h

Evaluate

Average = -6

This also represents the slope

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Answer:

Step-by-step explanation: it it D

(y2-y1)/(x2-x1)

ex:-1-(-3)/-1-(-2)=2

The following form has two parallel sides, and, in accordance with the provided assertion, its area is 21 cm².

Area is the entire amount of space occupied by a flattened (2-D) surface or form of an item. The area of a planar figure is the space that its perimeter encloses. The quantity of unit rectangles that completely encircle a closed figure's surface is its area. Square units such as cm² and m² are used to measure area.

The ratio will also be 1/2 * (bases 1 + base 2) * length since it is a trapezium.

So, 1/2 * ( 9+5) * 3

   = 1/2 * 14 * 3

   =  1/2 * 42

   =  21 cm²

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The largest angle of the triangle is ∠C = 66°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

Now , the measure of ∠A = measure of ∠B = x

And , the measure of ∠C = measure of ∠A + 9°

Substituting the values in the equation , we get

x + x + ( x + 9 ) = 180

On simplifying the equation , we get

3x + 9 = 180

Subtracting 9 on both sides of the equation , we get

3x = 171

Divide by 3 on both sides of the equation , we get

x = 57°

So , the measure of ∠A = 57°

Now , the measure of ∠C = 57 + 9 = 66°

Hence , the measure of ∠C of triangle is 66°

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The compound interest is $348,966.97 and the future value is $464,966.97.

percentage, a relative value indicating hundredth parts of any quantity.

We can use the formula for compound interest to calculate the future value of the investment:

[tex]FV=P(a1+r/n)^{nt}[/tex]

where:

P = the principal amount (the initial investment)$116,000

r = the annual interest rate (as a decimal)=0.0429

n = the number of times the interest is compounded per year=52

t = the number of years=34

Plugging in these values, we get:

FV = $116,000(1 + 0.0429/52)¹⁷⁶⁸

FV = $464,966.97

So the future value of the investment after 34 years is $464,966.97.

Compound interest = $464,966.97 - $116,000 = $348,966.97

Therefore, the compound interest is $348,966.97 and the future value is $464,966.97.

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In a linear equation. , $12,215 did he save in tax by using Schedule A .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                 Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Given,

      Taxable income with out deductions = $63,110

                     total deductions = $10,312

       the tax is given in the row 63.100 63,150 and in the column 'single' of the tax table is

                          tax = $12,215

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The perimeter of the figure after a dilation with a scale factor of 4 is

Suppose the initial measurement of a figure was x units.

And let the figure is scaled and new measurement is of y units.

Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.

Then we have:

[tex]s \times x = y\\s = \dfrac{y}{x}\\[/tex]

Thus, scale factor is the ratio of the new measurement to the old measurement.

Given;

The perimeter= 12units

Scale factor=4

Now,

Dilation with the given scale factor;

= 12*1/4

=12/4

=3

Therefore, dilation by the given scale factor will be 3.

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The value of x is 11.78.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

In a figure, the four angles sum must equal 360.

Now,

The four angles are:

6x + 7, 5x + 13, 12x + 9, and 73

Solve for x.

6x + 7 + 5x + 13 + 12x + 9 + 73 = 360

23x + 89 = 360

23x = 360 - 89

23x = 271

x = 11.78

Thus,

x is 11.78.

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Complete question:

In the figure measurement angle 1 is 6x + 7°, measurement angle 2 equals 5x + 13°, and measurement angle 3 equals 12x + 9° and measurement angle 4 equals 73°.

What is the value of x?

The minimum cost after assigning the jobs to different machines is 48. The solution has been obtained by using the cost function.

What is a cost function?

For some fixed factor prices, the cost function calculates the lowest cost of generating a specified level of output. The economic potential of a corporation is described by the cost function.

According to the cost function, the optimal assignment in order to minimise the total cost is by assigning:

Job J1 to machine M2 having a cost of 11

Job J2 to machine M3 having a cost of 12

Job J3 to machine M1 having a cost of 14

Job J4 to machine M4 having a cost of 11

From this, we get the total minimum cost as:

11 + 12 + 14 + 11 = 48

Hence, the minimum cost after assigning the jobs to different machines is 48.

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Answer:

77.4 (nearest tenth)

Step-by-step explanation:

76 is 100% of the original number.

To increase a number by 1.8% it will be 100% + 1.8% = 101.8% of the original number.

[tex]\begin{aligned}\implies \sf 101.8\%\; of\; 76&=\sf \dfrac{101.8}{100} \times 76\\\\&=\sf \dfrac{101.8 \times 76}{100}\\\\&=\sf \dfrac{7736.8}{100}\\\\&=\sf 77.368\\\\&=\sf 77.4\; (nearest\;tenth)\end{aligned}[/tex]

Therefore, the result when the number 76 is increased by 1.8% is 77.4 to the nearest tenth.

10 pounds of barley should be used by the cook to mix in with the 35 quarts of the vegetable broth.

lets say we know that there is a mix of 2 pounds of barley into 7 quarts of vegetable broth, so we can say that,

2:7 is the ratio used for the mix

similarly we can say,

let the pounds of barley into 35 quarts of vegetable broth used be x

x:35 because its given that there are 35 quarts used in the vegetable soup so we need to find the value of 'x'

then, 2/7=x/35, that is pounds/quarts

then, x= 2/7 × 5

then, x = 2×5

therefore we know that x = 10

so we can say that there are 10 pounds of barley used in the mix by the cook along with the 35 quarts of vegetable broth.

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Actual distance from Spokane to Missoula = 100 miles

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

Given,

On map one inch represents 20 miles

Distance between Spokane to Missoula on map = 5 inches

Actual distance = 5 × 20 = 100 miles

Hence, 100 miles is the actual distance from Spokane to Missoula.

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The functions are matched as follows -

y = √x ⇒  d. Square root

y = |x| ⇒  g. Absolute value

y = x² ⇒  h. Quadratic

y = 1/x² ⇒  f. Reciprocal Squared

y = 1/x ⇒  b. Reciprocal

y = x³ ⇒  a. Cubic

y = ∛x ⇒  e. Cube root

y = x ⇒  c. Linear

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The first function is given as -

y = √x

Since, this function contains a square root symbol, so it is a square root function.

The second function is given as -

y = |x|

Since, this function contains absolute value symbol, so it is a absolute value function.

The third function is given as -

y = x²

Since, this function contains power of 2 and x is squared, so it is a quadratic function.

The fourth function is given as -

y = 1/x²

Since, this function contains power of 2, x is squared and the value is reciprocal of x², so it is a reciprocal squared function.

The fifth function is given as -

y = 1/x

Since, this function contains reciprocal value of x, so it is a reciprocal function.

The sixth function is given as -

y = x³

Since, this function contains power of 3 and x is cubed, so it is a cubic function.

The seventh function is given as -

y = ∛x

Since, this function contains a cube root symbol, so it is a cube root function.

The second function is given as -

y = x

Since, this function contains y equal to x, so it is a linear function.

Therefore, all the different functions are identified.

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