Use the rules of exponents to simplify the expression. write the answer with positive exponents. Assume that all variables represent positive real numbers.

Answer:

C

Step-by-step explanation:

2:3 = x:60

3 → 60 (*20)

2*20=40

Answer:

40 green houses

Step-by-step explanation:

Because the ratio is given, you can use the criss-cross method.

2:3

?:60

All you do is multiply 60 by 2 then divide by 3

(60×2)/3=40

Answer:

Option B is the correct option.

Here,

Adjacent=15

Hypotenuse=17

Now,

\(cos \: theta = \frac{adjacent}{hypotenuse} \\ cos \: 28 = \frac{15}{17} \)

Hope this helps..

Good luck on your assignment..

Answer:

B. 15/17

Step-by-step explanation:

(see attached graphic for reference)

Because we have a right triangle (i.e one of the internal angles is 90 degrees), we can use trigonometry to solve

from the diagram, we can see that

cos 28° = adjacent length / hypotenuse

we can also see that the length adjacent to 28° = 15 units and the hypotenuse is 17 units,

hence, substituting these values into the equation:

cos 28° = 15 / 17   (answer)

edit: typo

Distance travelled by Ryan's family in 3 hours is d = 200 miles.

Determine the distance travelled by Ryan's family in 1 hour.

Answer: 66.667 miles

The volume of each cylinder is 1,017.4 yd³.

What is the volume of a cylinder?

The volume of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it. The formula r2h, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder.

Here, we have

Given: The volume of a cylinder can be found using this formula

V = πr²h

where r = radius and h = height

The cylinder shown has a radius of 9 inches and a height of 4 inches

Knowing this information we plug it into the formula

V = 3.14×(9)²(4)

V = 3.14×81×4

V = 1,017.4 yd³

Hence,  the volume of each cylinder is 1,017.4 yd³.

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total cost = 6.25 + 0.25 x

15.75 - 6.25 = 0.25 x

9.5 = 0.25 x

x = 38 prints

Answer:

2x + 3x + 7x = 288

12x = 288

x = 24

The largest number is therefore 7 * 24 = 168

Step-by-step explanation:

Answer:

Step-by-step explanation:

The tax on $155,000 is computed by adding the tax due in each bracket.

  total tax = (0.24)(155,000 -85,525) +(0.22)(85,525 -40,125) +(0.12)(40,125 -9,875) +(0.10)(9,875)

  = (0.24)(155,000) +(85,525)(-0.24 +0.22) +(40,125)(-0.22 +0.12) +(9,875)(-0.12 +0.10)

  = 0.24(155,000) -(0.02(85,525) +0.10(40,125) +0.02(9,875))

  = 37,200 -(1710.50 +4012.50 +197.50) = 37,200 -5920.50

  = 31,279.50

Taxes owed on $155,000 are $31,279.50.

__

The 80% rule says your retirement income should replace 80% of your pre-retirement income. If W is your pre-retirement annual wage, your retirement need is expected to be 0.80×W.

The 4% rule says your first-year withdrawal should be about 4% of your retirement savings (S). That is, we want ...

  0.80×W = 0.04×S

Solving for S, we find ...

  S = W×(0.80/0.04) = 20W

If the annual gross wage is 72,500, the retirement savings needed is predicted to be ...

  S = 20(72,500) = 1,450,000

Total retirement savings needed is $1,450,000 using these rules.

\(x^2 -8x-2=0\\\\x^2 -8x=2\\\\x^2 -8x+16=18\\\\(x-4)^2 =18\\\\x-4=\pm \sqrt{18}\\\\\boxed{x=4 \pm \sqrt{18}}\)

Answer:

Step-by-step explanation:

10 -2.95 = 7.05

the scarf cost $ 7.05

Answer:

4456646

Step-by-step explanation:

its that bc we add

Answer

The cost of one small bottle is $16.00

EXPLANATION

Problem Statement

The question tells us that Large bottles cost $5 more than smaller ones while 10 large bottles cost $30 less than 15 small ones. We are asked to find the cost of one small bottle.

Solution

To solve this question, we need to interpret the statements within the question and write them out as solvable equations. Thus, the steps we shall take are as follows:

Step 1: Analyze the statements and write them in form of equations.

Step 2: Solve the equations simultaneously

Step 1:

Statement 1:

"Large reusable bottles cost $5 more than small ones"

Statement 2:

"Ten large bottles cost $30 less than 15 small ones"

Now that we have our equations, we can proceed to solve for the cost of a small bottle S, by substitution.

Step 2:

Final Answer

The cost of one small bottle is $16.00

Ages of Tristan, Richard, and Pablo are in the order 6:7:4.

Detailed explanation:

Pablo is six years younger than Richard, seven years older than Tristan, and five years younger than Richard.

We can multiply the ratios of Pablo's age to Richard's age and Pablo's age to Tristan's age to determine the ratio of Tristan's age to Richard's age before determining the ratio of Tristan's age to Pablo's age.

These ratios add up to 6/7 * 5/4 = 30/28.

Pablo's age to Richard's age is 6:7, thus we may multiply this ratio by the age of Richard by Tristan's age to determine the age of Pablo, Richard, and Tristan.

Thus, the ratio of Pablo's age to Richard's age to Tristan's age is 6:7:4.

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To solve this problem one must be aware of the concepts of standard deviation and variance of raw data.

There is a direct formulae to calculate the variance of the data,

Variance = \(σ^{2} =\frac{Sigma(xi-m)^{2}}{n}\)

Now here we need to verify ∑x and ∑\(x^{2}\).

∑x = 21+19+15+32+27

     = 114

and ∑\(x^{2}\) = \(21^{2} +19^{2} +15^{2} +32^{2} +27^{2}\)

             = 441+361+225+1024+729

             = 2780

So, the given relation is true.

Now the variance of the given data by putting the values in the formulae is  equal to 45.2.

And Standard deviation=\(\sqrt{Variance}\)

                                     = \(\sqrt{45.2}\)

                                      = 6.72

And for population α²=36.16 and deviation=6.01.

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Answer:

-0.25, -0.15, -0.6

Step-by-step explanation:

- 1/4= -0.25.

Bigger number with negative = smaller number

I. The solution to the system of equations using Gaussian elimination is x = 1, y = -1, and z = 2.

II. For the LU-decomposition method, we need to have a square coefficient matrix, which is not the case in the given system. Therefore, we cannot directly apply the LU-decomposition method.

III. For this method to converge, the coefficient matrix must be diagonally dominant, which is not the case in the given system. Therefore, the Gauss-Jacobi method cannot be directly applied either.

IV. It requires the coefficient matrix to be diagonally dominant, which is not satisfied in the given system. Hence, the Gauss-Seidel method cannot be directly used.

I. Gaussian Elimination Method:

To solve the system of linear equations using Gaussian elimination, we perform row operations to reduce the system into upper triangular form. The augmented matrix for the given system is:

| 6 2 -1 | 4 |

| 1 5 1 | 3 |

| 2 1 4 |27 |

We can start by eliminating the coefficients below the first element in the first column. To do this, we multiply the first row by a suitable factor and subtract it from the second and third rows to eliminate the x coefficient below the first row. Then, we proceed to eliminate the x coefficient below the second row, and so on.

After performing the necessary row operations, we obtain the following reduced row-echelon form:

| 6 2 -1 | 4 |

| 0 4 2 | -1 |

| 0 0 3 | 6 |

From this form, we can easily back-substitute to find the values of x, y, and z. We have z = 2, y = -1, and x = 1.

II. LU-Decomposition Method:

LU-decomposition is a method that decomposes a square matrix into a product of two matrices, L and U, where L is lower triangular and U is upper triangular.

III. Gauss-Jacobi Method:

The Gauss-Jacobi method is an iterative numerical method to solve systems of linear equations.

IV. Gauss-Seidel Method:

Similar to the Gauss-Jacobi method, the Gauss-Seidel method is an iterative method for solving linear systems.

Therefore, out of the four methods mentioned, only the Gaussian elimination method can be used to solve the given system of linear equations.

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259.25π in² is the surface area of the cone

The surface area of a cone can be calculated using the formula SA = πr² + πrl

where r is the radius and l is the slant height.

Given that the diameter is 17 inches, the radius (r) is half of the diameter, which is 17/2 = 8.5 inches.

The slant height (l) is given as 22 inches.

Substituting these values into the formula:

Surface Area = π(8.5)² + π(8.5)(22)

= 72.25π + 187π

= 259.25π

Therefore, the surface area of the cone is 259.25π in²

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243 = the pages read on Saturday

243 - 53 = 190 = the pages read on Sunday

190 + 243 =  433 = total pages read

Answer = 433

the exact coordinates of the holes of this function are:

x=-1 and x=1, because the denominator can never be zero.

Step-by-step explanation:

The formula to find the interior angle of a polygon is 180(n - 2) over n.

So, we know that the interior angle of the polygon which is 120, therefore we can produce this equation, 180(n - 2) over 2 n, equals to 120.

Now we use algebric method to solve for n.

180n − 360 = 120n

60n = 360

n = 6

The six trigonometric functions of an angle θ in a right triangle are sine (sin θ), cosine (cos θ), tangent (tan θ), cotangent (cot θ), secant (sec θ) and cosecant (csc θ).

To find these functions for a given angle θ, we need to know the length of the sides of a right triangle with angle θ.

Given that the point (-5,12) is on the terminal side of θ, we can apply the Pythagorean Theorem to find the length of the sides of the triangle. The Pythagorean Theorem states that a² + b² = c² where a and b represent the lengths of the sides of the triangle and c is the length of the hypotenuse. Using the point (-5,12), we can solve for c, which is 13.

Therefore, the sides of the triangle have lengths 5, 12, and 13. We can now use these lengths to calculate the trigonometric functions of θ.

sin θ = 12/13

cos θ = 5/13

tan θ = 12/5

cot θ = 5/12

sec θ = 13/5

csc θ = 13/12

Therefore, the six trigonometric functions of θ are sin θ = 12/13, cos θ = 5/13, tan θ = 12/5, cot θ = 5/12, sec θ = 13/5 and csc θ = 13/12.

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Answer:

He pays income tax of 1175 a year

Step-by-step explanation:

Mr. Ekpeh Salary PY = 4700

so 4700 / 100% = 47

1% = 47

47x25% = 1175

so income tax = 1175 a Year

Answer:

touches

crosses

Step-by-step explanation:

\(x=a\) is said to be a zero of a function \(f(x)\) if \(f(a)=0\)

A zero say \(x=a\) has a "multiplicity" equal to \(n\), if the factor \((x-a)^n\) appears in the polynomial.

When a real zero \(x=a\) of a polynomial function \(f\) is of even multiplicity, the graph of \(f\) touches the x-axis at \(x=a\), and when it is of odd multiplicity, the

graph of \(f\) crosses the x-axis at \(x=a\).

The critical points for the given function f(x) are -√5 and √5.

so option d is the correct answer.

A critical point is the part of the domain of a function where the derivative is either equal to zero or the function is not differentiable.

Differentiate the given function f(x)=x/(x²+5)

f'(x)=((x²+5)-x(2x))/(x²+5)²

Using the Quotient Rule for differentiation.

A method for finding the derivative or differentiation of a function that is given as a ratio or division of two differentiable functions in calculus is known as the quotient rule.

We get f'(x)=5-x²/(x²+5)²

So the derivative is zero at -√5 and √5 and non differentiable at -√5

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From the given scenario, AB = [17 + 28, 47 + 58] = [23, 64]

To calculate the product of matrices XY, the number of columns in X must match the number of rows in Y. In this case, X has 1 column and Y has 2 rows, so the product XY is undefined.

A general example of this with matrices is:

Let A be a 2x3 matrix:

A = [1 2 3; 4 5 6]

Let B be a 1x2 matrix:

B = [7 8]

To calculate the product AB, we need the number of columns in A to match the number of rows in B.

In this case, A has 3 columns and B has 1 row, so the product AB is:

AB = [17 + 28, 47 + 58] = [23, 64]

P.S Your question is incomplete, so I showed how to calculate the product of matrices XY,

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Answer:

$%

Step-by-step explanation:

cause x to the square root of 27 x 9382 is equal to the penguin race that gives us $%

Glad i could help!

Answer:

The circle's circumference is approximately 106.81 centimeters.

Explanation:

The formula for the circumference of a circle is C = 2πr, where C is the circumference, π is pi (approximately 3.14), and r is the radius of the circle.

So, for a circle with a radius of 17 centimeters, its circumference can be found by:

C = 2πr

C = 2 x 3.14 x 17

C ≈ 106.81 cm

Therefore, the circumference of the circle is approximately 106.81 centimeters.

Answer:

b=53 degrees

Step-by-step explanation:

90 degrees - 37 degrees = 53 degrees