Find the inverse of the function
g(x)=2x+5
algebraically.

Answer:

Step-by-step explanation:

I'm not sure if this is completely correct, but:

We have this equation, logarithm base 10 of x, which is equal to y.

This equation can be reorganized like this: \(10^{y}\) = x, or 10 to the y power is equal to x.

y represents the power that 10 (the base) is raised to, while x represents the result of  \(10^{y}\) (the base to the power of y).

The total number of samples will be 1109 .

Given ,

Margin of error 0.02

Here,

According to the formula,

\(Z_{\alpha /2} \sqrt{pq/n}\)

Here,

p = proportions of scientist that are left handed

p = 0.09

n = number of sample to be taken

Substitute the values,

\(Z_{0.01} \sqrt{0.09 * 0.91/n} = 0.02\\ 2.33 \sqrt{0.09 * 0.91/n} = 0.02\\\\\\\)

n ≈1109

Thus the number of samples to be taken will be approximately 1109 .

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5/3 (a)(x)(b)(xx)(c)(a^3)

5/3 (a^4)(b)(c)(x^3)

-2.07 (a^2)(x^3)(a^2)(b)

-2.07 (a^4)(b)(x^3)

-7/6 (a^2)(x^3)(c)(a^2)(b)

-7/6 (a^4)(b)(c)(x^3)

Notice that only the first and third monomials (when simplified) contain the exact same variables with the same exponents. Therefore, those are the only two monomials we can add together.

(10/6 - 7/6)(a^4)(b)(c)(x^3) - 2.07(a^4)(b)(x^3)

(1/2)(a^4)(b)(c)(x^3) - (2.07)(a^4)(b)(x^3)

(a^4bx^3)(1/2c - 2.07) --- Factored form

Since this expression has two terms, it is a binomial.

Hope this helps!! :)

The volume of the cylinder is approximately 40,107.6 cubic yards.

What is the volume of the cylinder?

The formula for the volume of a right circular cylinder is:

\(V = \pi r^2h\)

The formula for the volume of a right circular cylinder is:

\(V = \pi r^2h\)

Substituting the given values:

V = 3.14 x 17.2² x 45.3

V = 3.14 x 296.84 x 45.3

V = 40,107.6152 cubic yards

Rounding to the nearest tenth:

V ≈ 40,107.6 cubic yards

Therefore, the volume of the cylinder is approximately 40,107.6 cubic yards.

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Answer: 42080.87328 or 42,080.9 rounded to the nearest tenth

Step-by-step explanation:

V=πr2

V= 3.14 x 17.2 x 45.3

V= 3.14 x 17.2 squared x 45.3

= 17.2 squared is 295.84

V= 3.14 x 295.84 x 45.3

V= 42,080.87328

round it to nearest tenth and get 42,080.9 yd

The correct equation for the circle of curvature.

\(a. [x - \pi /2]^2 + (y - 1)^2 = 1/625\)

To find the equation for the circle of curvature of the curve, we need to determine the center and radius of the circle. The circle of curvature is the locus of the centers of the osculating circles of the curve at various points.

The curvature of a curve r(t) = x(t) i + y(t) j is given by the formula:

\(K(t) = |(x'(t)y''(t) - y'(t)x''(t)) / [(x'(t)^2 + y'(t)^2)^{3/2})|\)

where prime denotes the derivative with respect to t.

First, let's find the derivatives of the given curve:

r(t) = t i + sin(5t) j

r'(t) = 1 i + 5cos(5t) j

r''(t) = -25sin(5t) i

x(t) = t

x'(t) = 1

y(t) = sin(5t)

y'(t) = 5cos(5t)

y''(t) = -25sin(5t)

Now, let's evaluate these derivatives at t = π/2:

x'(π/2) = 1

y'(π/2) = 5cos(π/2) = 5(0) = 0

x''(π/2) = 0

y''(π/2) = -25sin(π/2) = -25

Substituting these values into the curvature formula:

\(K(\pi /2) = |(1)(-25) - (0)(0) / [(1^2 + 0^2)^{3/2}]|\\= |-25 / 1^{3/2}|\\= 25\)

The radius of curvature (ρ) is the reciprocal of the curvature:

ρ = 1 / κ(π/2)

= 1 / |-25|

= 1/25

The center of the circle of curvature lies on the normal line to the curve at the point [π/2, 1].

The normal line is perpendicular to the tangent line, which has the direction vector given by r'(π/2) = 1 i + 0 j = i.

The normal line passing through the point [π/2, 1] is given by the equation:

r(t) = [π/2, 1] + t i

The center of the circle lies on this line, so we can express it as:

C = [π/2, 1] + t i

To find t, we substitute the point [π/2, 1] into the equation of the line:

[π/2, 1] = [π/2, 1] + t i

This implies t = 0.

Therefore, the center of the circle is C = [π/2, 1].

Now, we have the center and radius of the circle, so we can write its equation in the form:

\([(x - \pi /2)^2 + (y - 1)^2] = (1/radius of curvature)^2\\[(x - \pi /2)^2 + (y - 1)^2] = (1/25)^2\\[(x - \pi /2)^2 + (y - 1)^2] = 1/625\)

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Answer:

Solve this equation. Enter your answer in the box. 75 â€"" 3. 5y â€"" 4y = 4y 6.

The answer of this question is equation [-6x+4y=16].

An equation is a mathematical statement that shows the equality between two expressions, typically separated by an equal sign. It can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of solving an equation is to find the value of the variable that makes the equation true.

In mathematics, a system refers to a collection of mathematical objects or entities that are related or interconnected in some way.

System A

5x-y=-11

3x-2y=-8

System B

5x-y=-11

-2(3x-2y)=-8×(-2)

5x-y=-11

-6x+4y=16

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There are the number of pods of peas are  = 38

A number is split in the straightforward action of division. It's simpler to visualize it as a set of items being distributed to a certain group of individuals, as in the scenario given above. Naturally, in the interest of fairness, you should always offer each person the same amount.

One of the four fundamental operations of arithmetic, or how to mix numbers to create new ones, is division. Addition, subtraction, and multiplication are the other operations.

total number of peas = 288

peas have per pod  = 6

total number of pods required  = 288/6

                                                    = 38

there are the number of pods of peas are  = 38

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I understand that the question you are looking for is:

George Mendel is examining peas to try to understand how traits are passed from parents to offspring. Today Gregor has 228 peas to examine . The pods have 6 peas per pod. How many pods of peas are there?

The perimeter of the figure or the amount of black cord required is given by P = 110.18 feet

The amount of fabric required for each figure is given by A = 222.985 feet²

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P of rectangle = 2 ( Length + Width )

Given data ,

Let the perimeter of the figure be represented as P

Let the amount of fabric required be A = area of the figure

Now , the length and width of the perimeter of rectangle are 16 feet and 10 feet respectively

The height and base of the triangle is 1.73 feet and 2 feet respectively

The side length of the square is 7 feet

The circle at the center has a diameter of 3 feet so the radius is 1.5 feet

Now , the perimeter of rectangle P = 2 ( L + B ) = 2 ( 16 + 10 )

The perimeter of rectangle = 2 x 26 = 52 feet

The area of rectangle = 16 x 10 = 160 feet²

The perimeter of 4 triangles = 4 x ( 3 x 1.73 ) = 20.76 feet

The area of 4 triangles = 4 ( ( 1/2 ) x 1.73 x 2 ) = 6.92 feet²

The circumference of the circle = 2πr = 2 x 3.14 x 1.5 = 9.42 feet

The area of circle = πr² = 3.14 x 1.5 x 1.5 = 7.065 feet²

The perimeter of square = 4a = 4 x 7 = 28 feet

The area of square = a² = 49 feet²

Now , the amount of black cord required = perimeter of rectangle + perimeter of 4 triangles + circumference of the circle + perimeter of square

The amount of black cord required P = 110.18 feet

And , the amount of fabric required A = area of rectangle + area of 4 triangles + area of circle + area of square

The amount of fabric required A = 222.985 feet²

Hence , the amount of black cord required is 110.18 feet and the amount of fabric required is 222.985 feet²

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The missing Value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

The missing value that, when multiplied by 5/3^4, gives the result of 5^4, we can set up the equation:

(5/3^4) * x = 5^4

To solve for x, we can simplify both sides of the equation. First, let's simplify the right side:

5^4 = 5 * 5 * 5 * 5 = 625

Now, let's simplify the left side:

5/3^4 = 5/(3 * 3 * 3 * 3) = 5/81

Now we have:

(5/81) * x = 625

To solve for x, we can multiply both sides of the equation by the reciprocal of 5/81, which is 81/5:

(81/5) * (5/81) * x = (81/5) * 625

On the left side, the fraction (81/5) * (5/81) simplifies to 1, leaving us with:

1 * x = (81/5) * 625

Simplifying the right side:

(81/5) * 625 = 13125

Therefore, the missing value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

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initial class boundary of 1.5

ending class boundary of 13.5

Number of classes: 6

Class width: Subtract initial class boundary from ending class boundary and divide the result into the number of classes:

Classes:

1.5 - 3.5

3.5 - 5.5

5.5 - 7.5

7.5 - 9.5

9.5 - 11.5

11.5 - 13.5

Order the given data to find easily the frequency of each class:

Then, you get frequencies of:

1.5 - 3.5: 4

3.5 - 5.5: 2

5.5 - 7.5: 2

7.5 - 9.5: 2

9.5 - 11.5: 6

11.5 - 13.5: 3

And you get the next histogram:

The winner's probability is 0.064.

Given:

The odds of winning box A are 40%, which is 0.4 percent.

The odds of winning box B are 1-4%, which is 0.6 percent.

The odds of winning box B are 6%, which is 0.06 percent.

Find:

Calculation of the winner's probability:

The probability of winning is equal to the probability of winning box A, the probability of winning box B, and the probability of winning box A. The probability of winning is equal to [0.4][0.07] and [0.6][0.06]. The probability of winning is equal to 0.028 and the probability of winning is equal to 0.036.

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Answer: the price of one senior citizen ticket is $10, and the price of one student ticket is $5.

Step-by-step explanation:

Let's assume the price of one senior citizen ticket is 's' dollars and the price of one student ticket is 't' dollars.

According to the given information, on the first day, the school sold 7 senior citizen tickets and 11 student tickets, totaling $125. This can be expressed as the equation:

7s + 11t = 125 ---(1)

On the second day, the school sold 14 senior citizen tickets and 8 student tickets, totaling $180. This can be expressed as the equation:

14s + 8t = 180 ---(2)

We now have a system of two equations with two variables. We can solve this system to find the values of 's' and 't'.

Multiplying equation (1) by 8 and equation (2) by 11, we get:

56s + 88t = 1000 ---(3)

154s + 88t = 1980 ---(4)

Subtracting equation (3) from equation (4) eliminates 't':

(154s + 88t) - (56s + 88t) = 1980 - 1000

98s = 980

s = 980 / 98

s = 10

Substituting the value of 's' back into equation (1), we can solve for 't':

7s + 11t = 125

7(10) + 11t = 125

70 + 11t = 125

11t = 125 - 70

11t = 55

t = 55 / 11

t = 5

Therefore, the price of one senior citizen ticket is $10, and the price of one student ticket is $5.

Answer:

\(\frac{5x-3}{4}\)

Step-by-step explanation:

\(x=\frac{4y+3}{5} \\ 5x=4y+3\\ 5x-3=4y\\ \frac{5x-3}{4} =y\)

The volume of the triangular prism is 216 cubic meters.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.

Calculate the area of the triangular base.

The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.

Plugging in the values, we get:

Area = (1/2) * 8 meters * 9 meters = 36 square meters.

Multiply the area of the base by the length of the prism.

The length of the prism is given as 12 meters.

Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.

Adjust for the shape of the prism.

Since the prism is a triangular prism, we need to divide the volume by 2.

Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.

Therefore, the volume of the triangular prism is 216 cubic meters.

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To modify and graph the system of inequalities:

Modify the first inequality:

Multiply both sides of the inequality by -1 to change the direction of the inequality sign:

-(x + 5y) < 10

Graph the modified inequalities on a coordinate plane:

For the first inequality, plot the line x + 5y = -10. To do this, find two points that satisfy the equation (e.g., when x = -10, y = 2 and when x = 0, y = -2). Draw a dashed line passing through these points to represent the inequality.

For the second inequality, graph the line x + y = 4. Find two points that satisfy the equation (e.g., when x = 4, y = 0 and when x = 0, y = 4). Draw a solid line passing through these points to represent the inequality.

Shade the region that satisfies both inequalities. Since the second inequality has the symbol ≤, shade the region below the line x + y = 4.

The shaded region where the two lines intersect represents the solution to the system of inequalities.

Note: The instructions provided here assume a two-dimensional graph. However, without specific values, it is not possible to draw an accurate graph.

The process described above should be followed once the specific values are provided.

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The range of lengths is given by the inequality:

4.1 in ≤ L ≤ 4.5 in

We know that the length of a manufactured ceramic bead is 4.3 centimeters, with an acceptable error of 0.2 inches.

This means that the length of the ceramic bead can be, at most, 0.2 inches away (lower or upper) from 4.3 in.

Then the smaller length allowed is:

4.3 in - 0.2 in = 4.1 in

The largest length allowed is:

4.3 in + 0.2in = 4.5in

Then the range of lengths is given by the inequality:

4.1 in ≤ L ≤ 4.5 in

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The otiginal price will be the 100% and the sale price will be the 100% minus the 30% so will be the 70%, so with this information we can use a rule of 3 to solve the problem so:

so the equation will be:

The width of Josephine's garden is 2, and the length is represented by the expression (x^2 - 3). The given expression for the area of Josephine's garden is 2x^2 - 6 square feet.

To determine the length and width of the garden, we need to factorize the expression.

The expression 2x^2 - 6 can be factored as follows:

2x^2 - 6 = 2(x^2 - 3).

From the factored form, we can see that the coefficient 2 represents the width of the garden, while the expression (x^2 - 3) represents the length of the garden. Therefore, the width of the garden is 2, and the length is given by (x^2 - 3).

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For the ratios of the angles;

Sine, cosine, and tangent are trigonometric functions used to calculate the ratios of the sides of a right triangle. The side opposite the right angle is called the hypotenuse, while the other two sides are called the adjacent and opposite sides.

Let the hypotenuse be X

Angle A;

Sine A= D/X

Cos A = M/X

Tan A = D/M

Angle B;

Sin B = M/X

Cos B = D/X

Tan B = M/D

The e angle in question may be measured in radians or degrees.

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Answer:

11/20

Step-by-step explanation:

5 cents is worth $0.05.

A quarter is worth $0.25.

A dime is worth $0.10

A nickel is worth $0.05

A penny is worth $0.01

In total there are 40 coins in the jar.

The coins that are worth more than $0.05 dollars are the dimes and quarters, so there are 22 coins worth more than $0.05.

Therefore, the probability of of picking a coin worth more than 5 cents is:

22 / 40 = 11/20

Answer:

2(quotient of x) + 2..............

Answer:

Y=5/1x+15

Step-by-step explanation:

I know this is old, but no one answered it so I thought I would

Answer:

it would take 3,000 neyland stadiums to take 300milion people is rounded i hope this helps

Step-by-step explanation:

Answer is The smaller angle is 35°.

To solve for the acute angles in a right triangle when sin(5x)° = cos(3x + 2)°, we need to use trigonometric identities.

Recall that sin(x) = cos(90 - x) for any angle x. Using this identity, we can rewrite sin(5x)° as cos(90 - 5x)°.

Similarly, cos(x) = sin(90 - x) for any angle x. Using this identity, we can rewrite cos(3x + 2)° as sin(90 - (3x + 2))°, which simplifies to sin(88 - 3x)°.

Now we have cos(90 - 5x)° = sin(88 - 3x)°. Since these two expressions are equal, we can set them equal to each other and solve for x:

cos(90 - 5x)° = sin(88 - 3x)°

sin(5x)° = sin(88 - 3x)°

5x = 88 - 3x

8x = 88

x = 11

Therefore, the acute angles in the right triangle are 5x° and 90 - 5x°, or 55° and 35°. The smaller angle is 35°.

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The nonsingular matrix p such that `p^-1ap` is diagonal is p = [2 -1 -1; 1 0 1; 1 1 0].

Given a matrix A `a = [ 2 -2 3; 0 3 -2; 0 -1 2]`.

Steps to diagonalize a matrix: `Set up the matrix `P` such that the eigenvectors are the columns of `P`To get the diagonalized matrix `D`, we use `P^-1 * A * P = D`.

We know that for a diagonal matrix D to exist, the matrix A must have three linearly independent eigenvectors.

The determinant of the matrix is also non zero, which means the matrix is invertible.

Let us first compute the eigenvalues of the matrix `A` by solving for det(A - λI) = 0 where `λ` is the eigenvalue of `A`.

The characteristic equation of the matrix `A` is given by: |A - λI| = 0

where `λ` is the eigenvalue of `A` and `I` is the identity matrix.

|A - λI| = |2 - λ -2 3 -2 - λ 0 -1 2 - λ|

          = (λ - 1)(λ - 2)^2

          =0

On solving the equation we get the eigenvalues of the matrix `A`.

Eigenvalues of `A` are `λ1 = 1,  λ2 = 2,  λ3 = 2`.

Let us now compute the eigenvectors of the matrix `A`.

For each eigenvalue, we have to solve the system of linear equations given by: (A - λI) X = 0

where `X` is the eigenvector.

For `λ1 = 1` we have (A - λ1I )X = 0(2 - 1 -2 3 -2 - 1 0 -1 2 - 1) X

                                               = 0X

                                               = [2; 1; 1]

For `λ2 = 2` we have(A - λ2I) X = 0(2 - 2 -2 3 -2 - 2 0 -1 2 - 2) X

                                                 = 0X

                                                 = [-1; 0; 1]

For `λ3 = 2` we have(A - λ3I) X = 0(2 - 2 -2 3 -2 - 2 0 -1 2 - 2) X

                                                 = 0X

                                                 = [-1; 1; 0]

The eigenvalues of the matrix `A` are `λ1 = 1, λ2 = 2, λ3 = 2`.

The eigenvectors of the matrix `A` are

`X1 = [2; 1; 1],

X2 = [-1; 0; 1],

X3 = [-1; 1; 0]`

We can now set up the matrix `P` by using the eigenvectors as columns.

That is `P = [X1 X2 X3]`.P = [2 -1 -1; 1 0 1; 1 1 0]

The inverse of the matrix `P` is given by `P^-1 = 1/6 * [1 1 1; -1 -2 1; -1 1 -1]`.

We can now compute `P^-1 * A * P` to get the diagonalized matrix `D`.

D = P^-1 * A * P = 1/6 * [1 1 1; -1 -2 1; -1 1 -1] * [2 -2 3; 0 3 -2; 0 -1 2] * [2 -1 -1; 1 0 1; 1 1 0]= diag(1,2,2).

Therefore, the nonsingular matrix p such that `p^-1ap` is diagonal is p = [2 -1 -1; 1 0 1; 1 1 0].

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