Translate the following statement into a mathematical equation:Five times a number, minus three, is twelve.5( n - 3) = 125 n = 12 - 35 - 3 n = 125 n - 3 = 12

Answer:

(\(\sqrt[5]{x}\))^7

Step-by-step explanation:

to cancel out the radical you do the exponent inside and divide it by the out side one so it will be 7/5 so make it x to the expontent of 7/5 and to do rational exponets it will be (^5radicalx)^7

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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When sales terms, customer creditworthiness, and accounting methods are constant, the percentage change in sales and the percentage change in accounts receivable should be about equal.

A customer is known to be one who can afford to pay for the product that they bought is said to be one who is creditworthy.

In a real world a person can extend as much credit to their customer as they can afford. When sales terms, customer creditworthiness, and accounting methods are said to not change, the percentage change in sales and that of accounts receivable should be about equal.

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Answer:

Hey!

I think the answer is B

Answer:

Width = 6k²

Length = 5k+1

Step-by-step explanation:

Given the area of a rectangle expressed as

A = 30k³ + 6k²

Get the greatest common factor

30k³ = (2 * 3 * k²) * k * 5

6k² = (2 * 3 * k²)

The common factor is the value in bracket i.e 2 * 3 * k² = 6k²

Width of the rectangle = 6k²

Get the length

A = LW

L = A/W

L = 30k³ + 6k²/6k²

L = 6k²(5k+1)/6k²

L = 5k + 1

Hence the length L = 5k+1

The stochastic matrix with columns and rows labeled S, M, and L that describes the transitions is:

| 0.3  0.5  0.4 |

| 0.7  0.5  0.1 |

| 0.0  0.0  0.5 |

The (i, j) entry in this matrix represents the probability of moving from state i to state j.

The Initial Distribution Matrix on Monday is:

| 0.7 |

| 0.2 |

| 0.1 |

This represents the proportion of people who have a strenuous, moderate, and light workout on Monday.

To find the percentage of people who have a light workout on Tuesday, we need to multiply the initial distribution matrix by the stochastic matrix twice:

| 0.3  0.5  0.4 |   | 0.7 |   | 0.35 |

| 0.7  0.5  0.1 | x | 0.2 | = | 0.32 |

| 0.0  0.0  0.5 |   | 0.1 |   | 0.33 |

So, 33% of people will have a light workout on Tuesday.

To find the percentage of people who have a strenuous workout on Wednesday, we need to multiply the initial distribution matrix by the stochastic matrix three times:

| 0.3  0.5  0.4 |   | 0.7 |   | 0.451 |

| 0.7  0.5  0.1 | x | 0.2 | x | 0.296 |

| 0.0  0.0  0.5 |   | 0.1 |   | 0.253 |

Therefore, 45.1% of people will have a strenuous workout on Wednesday.

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Answer:

---------------------------------

Answer:

$582.68

Step-by-step explanation:

Total amount will be,

→ $266.63 + $317.29 + $62.78

→ 266.63 + 380.07

→ $646.7

Then the final price will be,

→ ($646.7 - 15%) + 6%

→ (646.7 - (646.7/100) × 15) + 6%

→ (646.7 - 97.005) + 6%

→ 549.695 + (549.695/100) × 6

→ 549.695 + 32.9817

→ 582.6767

→ $582.68

Hence, the answer is $582.68.

We can use unit conversion to find the value of $1 in Euros:

\begin{aligned}

£1 &= $1.41 \\

\frac{£1}{1.15} &= \frac{$1.41}{x} \\

x &= \frac{$1.41}{\frac{£1}{1.15}} \\

&= $1.7278

\end{aligned}

Therefore, $1 is equal to €1.7278.

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:

r^2 - 2r - 3 = 0

Factoring, we get:

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

So the roots are r = 3 and r = -1.

The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:

y_h = c1e^3x + c2e^(-x)

To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = Ae^4x

Taking the first and second derivatives of y_p, we get:

y_p' = 4Ae^4x

y_p'' = 16Ae^4x

Substituting these into the original differential equation, we get:

16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x

Simplifying, we get:

5Ae^4x = e^4x

So:

A = 1/5

Therefore, the particular solution is:

y_p = (1/5)*e^4x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^3x + c2e^(-x) + (1/5)*e^4x

b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:

r^2 + r - 2 = 0

Factoring, we get:

(r + 2)(r - 1) = 0

So the roots are r = -2 and r = 1.

The general solution to the homogeneous equation y'' + y' - 2y = 0 is:

y_h = c1e^(-2x) + c2e^x

To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax + B)e^x

Taking the first and second derivatives of y_p, we get:

y_p' = Ae^x + (Ax + B)e^x

y_p'' = 2Ae^x + (Ax + B)e^x

Substituting these into the original differential equation, we get:

2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x

Simplifying, we get:

3Ae^x = 3xe^x

So:

A = 1

Therefore, the particular solution is:

y_p = (x + B)e^x

Taking the derivative of y_p, we get:

y_p' = (x + 2 + B)e^x

Substituting back into the original differential equation, we get:

(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x

Simplifying, we get:

-xe^x - Be^x = 0

So:

B = -x

Therefore, the particular solution is:

y_p = xe^x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^(-2x) + c2e^x + xe^x

c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:

r^2 - 9r + 20 = 0

Factoring, we get:

(r - 5)(r - 4) = 0

So the roots are r = 5 and r = 4.

The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:

y_h = c1e^4x + c2e^5x

To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax^2 + Bx + C)e^4x

Taking the first and second derivatives of y_p, we get:

y_p' = (2Ax + B)e^4x + 4Axe^4x

y_p'' = 2Ae^4x +

Answer:

Following are the responses to the given question:

Step-by-step explanation:

\(Null \ H_{yp}: \mu_{men} = \mu_{women}\\\\Alt \ Hyp: \mu_{men} \neq \mu_{women}\\\\Std\ Error\ (SE) = \sqrt{(\frac{s_1^2}{n_1}) + (\frac{s_2^2}{n_2})} \\\\\)

                          \(= \sqrt{(\frac{0.62}{90}) + (\frac{0.52}{100})} \\\\= 0.08\)

\(test\ statistic \ t = \frac{(x_1 - x_2)}{SE} = \frac{(8.4 - 8.5)}{0.08} = -1.25\)

Degrees of freedom

\(= \frac{(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2})^2}{\frac{(\frac{s_1^2}{n_1})^2}{(n_1 - 1)}} + \frac{(\frac{s_2^2}{n_2)^2}}{(n_2 - 1)} \\\\= 174\)

Considering a degree of 5% importance

T for df critical value = 174 and sig level = 0.05 is +1.973

Let area of refusal shall be  t < -1.973 or t > +1.973

Because statistical tests weren't in the refusal zone, they may not deny that zero but find that perhaps the argument how both women and men undergo med school is considerably different lengths of time is not significantly supported.

Answer:

√38

Step-by-step explanation:

√38

step 1: Check which squared numbers can be multiplied by another number to get 38.

Start with these numbers: 4, 9, 16, and 25

Step 2: Testing out the numbers

√25 × __ = 25 can't be divided by 38

√16 × ___ = 16 can't be divided by 38

√9 × ____ = 9 can't be divided by 38

√4 × ____= 4 can't be divided by 38

Step 3: Answer

After trying the square root numbers that could possibly work with √38 none work; which means √38 can't be simplified. So the answer is √38

I hope this helps!

Answer:

25

Step-by-step explanation:

Count all the squares on the edge.

Answer:

29cm

Step-by-step explanation:

The range of g is bounded between 1 - 2M and 1, but it may not include all values in that interval, depending on the range of f.

The range of function g depends on the range of the function f.

Let's start by assuming that we know the range of f.

If the range of f is Rf, then the range of -2f is the set {-2y | y ∈ Rf}, which is just the set of all numbers that can be obtained by multiplying an element of Rf by -2.

Finally, we add 1 to each of these values to get the range of g. Therefore, the range of g is:

Rg = {1 - 2y | y ∈ Rf}

In other words, the range of g is obtained by taking the range of f, multiplying each element by -2, and adding 1 to each result.

If we don't know the range of f, we can still say something about the range of g. Specifically, we know that g(x) can never be greater than 1 (since the largest value that -2f(x) can take is 0, and adding 1 to 0 gives us 1), and g(x) can never be less than 1 - 2M, where M is the largest possible value that f(x) can take on. In other words, the range of g is bounded between 1 - 2M and 1, but it may not include all values in that interval, depending on the range of f.

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Answer:

Step-by-step explanation:

\(y=(\frac{1}{g} )x\)

Constant up a proportionally is  \(\frac{1}{g}\).

Answer:

may 6th

Step-by-step explanation:

2+3=5 so if they when on the 1st and 2 +3=5 1+5=6

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

The measure of Angle C is approximately 26°.

A, B, C are vertices of a triangle, where AB = 8 cm, BC = 6 cm. To determine the measure of angle C, we need to use the cosine rule.

The cosine rule states that the square of one side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the other two sides and the cosine of the angle between them.

Mathematically, we can represent it as follows:a² = b² + c² - 2bc cos(A)where a is the side opposite to angle A, b is the side opposite to angle B, c is the side opposite to angle C.

In this case, we have AB = c = 8 cm, BC = a = 6 cm, and AC = b. We need to find the measure of angle C, which is represented as cos(C).

Using the cosine rule, we can write the equation as follows:$$\begin{aligned} b^2 &= c^2 + a^2 - 2ca\cos(C) \\ \Right arrow b^2 &= 8^2 + 6^2 - 2 \times 8 \times 6 \cos(C) \\ \Right arrow b^2 &= 64 + 36 - 96 \cos(C) \\ \Right arrow b^2 &= 100 - 96 \cos(C) \end{aligned}$$We know that b is a positive length. Hence, b² > 0 or 100 - 96 cos(C) > 0. Solving for cos(C),  

we get: cos(C) < 100/96cos(C) < 1.0417Using a calculator, we can determine the inverse cosine of 1.0417 as:cos⁻¹(1.0417) = 0.4569 radians = 26.201° (rounded to the nearest degree)

Therefore, the measure of angle C is approximately 26°.

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The total volume of the air space of spherical ball is A = 12.265625 inches³

Given data ,

Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.

The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.

The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.

The formula for the volume of a cylinder is:

V = πr²h

V = ( 3.14 ) ( 1.25 )² ( 7.5 )

V = 36.796875 inches³

where V is the volume, r is the radius, and h is the height.

So, the volume of the one ball is:

V₁ = ( 4/3 )π(1.25)³

V₁ = 8.177083 inches³

The total volume of three balls is = volume of 3 spherical balls

V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches

Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³

A = 12.265625 inches³

Hence , the volume of air space is A = 12.265625 inches³

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The equation of the polynomial equation is P(x) = 4/5(x - 1)^2(x + 5)

Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators

The given parameters are

Degree of polynomial = 3

x = 1 is a zero of multiplicity 2

x = -5 is a zero of multiplicity 1

The sum of multiplicities of the polynomial equation must be equal to the degree.

This means that the multiplicity of the zero -5 is 1 and the multiplicity of the zero 1 is 2

The equation of the polynomial is then calculated as

P(x) = a(x - zero)^ multiplicity

So, we have

P(x) = a(x - 1)^2 * (x + 5)

The y-intercept is y=-4

This gives

a(0 - 1)^2 * (0 + 5) = 4

So, we have

a = 4/5

Substitute a = 4/5 in P(x) = a(x - 1)^2 * (x + 5)

P(x) = 4/5(x - 1)^2 * (x + 5)

Hence, the equation of the polynomial equation is P(x) = 4/5(x - 1)^2 * (x + 5)

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Answer:

87

Step-by-step explanation:

= 17 1/2 ÷ 1/5

= 35/2 (improper fraction should be used as a dividend) × 5/1 (the divisor will be reciprocal and the operation will be multiplication)

= 175/2

= 87 1/2

Since the question is how many ⅕, the fraction will not be included.

Complete Question:

Annette and Rose went to an orchard to pick pears. Annette picked \(8\frac{1}{6}\)

pounds of pears and Rose picked\(6\frac{1}{8}\) pounds. How much more did Annette pick than Rose? Write your answer as a reduced mixed number.

Answer:

Annette picked \(2\frac{1}{24}\) pounds of pears more than Rose

Step-by-step explanation:

Pounds of pears picked by Annette = \(8\frac{1}{6}\)

Pounds of pears picked by Rose =  \(6\frac{1}{8}\)

To get the difference in the pounds of pears picked by Annette and Rose, we will do a simple subtraction:

Difference in the pounds of pears picked = \(8\frac{1}{6} - 6\frac{1}{8}\)

\(= 2(\frac{1}{6} - \frac{1}{8})\\= 2\frac{4 - 3}{24} \\= 2\frac{1}{24}\)

Answer: The length of the prism is 8 yards

Step-by-step explanation:

First, take the volume of the prism, divide it by the width (2 1/2). Once you get that divide that answer by height (5 3/4) getting you the length of the prism (8 yards)

The perimeter of a circle's quadrants with a diameter of 28 cm would be 22 cm.

1. The diameter of a circle is a straight line passing through the center and touching two points on the circumference.

2. Given that the diameter is 28 cm, we can find the radius by dividing the diameter by 2: 28 cm / 2 = 14 cm.

3. The perimeter of a circle is the total distance around its circumference. We can find the circumference using the formula C = 2πr, where C is the circumference and r is the radius.

4. Plugging in the radius we found earlier, the circumference of the circle is C = 2π(14 cm).

5. Simplifying the equation, we get C = 28π cm.

6. However, we only need to find the perimeter of one quadrant of the circle, which is a quarter of the full circumference.

7. To find the perimeter of the quadrant, we divide the circumference by 4: (28π cm) / 4 = 7π cm.

8. Approximating the value of π to 3.14, the perimeter of the quadrant is approximately 7(3.14) cm.

9. Calculating the approximate value, the perimeter of the quadrant is 21.98 cm.

10. Rounding to the nearest whole number, the perimeter of the quadrant is approximately 22 cm.

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Answer:

Option 2.

Step-by-step explanation:

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: \((- \infty} ,0)\) ∪ \((0, \infty} )\)

Range: \((- \infty} ,0)\)∪\((0, \infty} )\)

At a price of $3, the total revenue will be the greatest, and the company will sell 3 units at that price.

To find the total revenue at each price, we can multiply the price by the corresponding quantity.

Price        Quantity          Total Revenue

$6                0                      $0

$5                 1                       $5

$4                 2                       $8

$3                 3                        $9

$2                 4                         $8

$1                  5                          $5

To find the price at which total revenue is the greatest, we look for the highest value in the Total Revenue column.

In this case, the highest total revenue is $9, which occurs when the price is $3.

At a price of $3, the company will sell 3 units (as indicated in the Quantity column).

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Answer:

Step-by-step explanation:

Answer:

The equation of the sraight line  3x- y+ 6 =0

Step-by-step explanation:

Explanation:-

Given that the gradient of the function

   |gradf| = 3  and point (-1,3)

Given that the slope of the line

 m = 3

The equation of the straight line passing through the point(-1,3) and slope m =3

\(y -y_{1} = m(x-x_{1} )\)

y-3 = 3(x-(-1))

y-3 = 3x+3

3x +3-y+3=0

3x- y+ 6 =0

Final answer:-

The equation of the sraight line  3x- y+ 6 =0

Answer:

perdón yo no hablo inglés