The selling price for a classic speedboat is $12,000, which is $2500 less than two times its original price. What was the original price of the speedboat?

For the function y = 4x⁵, the value of d⁴y/dx⁴ = 320x.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. We can write -

y = f(x)

y' = dy/dx = (d/dx)[f(x)]

We have the following function -

y = 4x⁵

The given function is -

y = 4x⁵

dy/dx = 20x⁴                             {y = xⁿ, then y' = nxⁿ ⁻ ¹}

d²y/dx² = 80x³

d³y/dx³ = 160x²

d⁴y/dx⁴ = 320x

Therefore, for the function y = 4x⁵, the value of d⁴y/dx⁴ = 320x.

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The average rate of change is given by -2/5. The correct option is (d).

A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

The given graph shows different values of y at x = 4 and x = 14 as follows,

At x = 4, y = 7

And at x = 14, y = 3.

Now, the average rate of change can be determined by taking the ratio of the difference of the values of y to that of x as follows,

(3 - 7)/(14 - 4)

= -4/10

= -2/5

Hence, the average rate of change x = 4 to x = 14 is given as -2/5.

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The other roots of the cubic equation p(x) = 24·x³ - 46·x³ + 29·x - 6 are;

x = 1/2

x = 3/4

A cubic equation is an equation  that has 3 as the highest index.

The specified polynomial in the question is presented as follows;

P(x) = 24·x³ - 46·x² + 29·x - 6

The solution of the equation is; x =  (2/3)

Therefore, (x - 2/3) is a factor of the equation and we get;

(24·x³ - 46·x² + 29·x - 6) ÷ (x - 2/3)  has a remainder of 0

Dividing the above expression using long division, we get;

                    24·x²  - 30·x + 9

(x - 2/3)  [tex]{}[/tex]     |(24·x³ - 46·x² + 29·x - 6)

               [tex]{}[/tex]     24·x³ - 16·x² + 29·x  - 6

                [tex]{}[/tex]              -30·x²

            [tex]{}[/tex]                   -30·x² + 20·x

                          [tex]{}[/tex]                      9·x - 6

                        [tex]{}[/tex]                        9·x - 6

The other real roots of the specified equation can be found as follows;

The equation for the roots is; P(x) = 24·x³ - 46·x² + 29·x - 6 = 0

From the above long division, therefore;

24·x³ - 46·x² + 29·x - 6 = (24·x²  - 30·x + 9) × (x - 2/3) = 0

Which indicates; (24·x² - 30·x + 9) = 0 or (x - 2/3) = 0

The other solution are;

24·x³ - 30·x + 9 = 0

3·(·8·x² - 10·x + 3) = 0

8·x² - 10·x + 3 = 0

Solutions for the above equation in the form; a·x² + b·x + c = 0 can be obtained using the quadratic formula as follows;

The quadratic formula; x = [tex]\dfrac{-b\pm\sqrt{b^2 - 4\cdot a\cdot c} }{2\cdot a}[/tex]

By comparing the equation, 8·x² - 10·x + 3 = 0 to the equation, a·x² + b·x + c = 0, we get;

a = 8, b = -10, and c = 3

Therefore;

x = (10 ± √((-10)² - 4 × 8 × 3))/(2 × 8)

((-10)² - 4 × 8 ×3) = 2

Therefore;

x = (10 ± √((-10)² - 4 × 8 × 3))/(2 × 8) = (10 ± 2)/(16)

x = 3/4, and x = 1/2

Therefore, the other other roots in increasing sequence are;

x = 1/2 and x = 3/4

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Using the secant-secant theorem,

[tex]\frac{13x+7-60}{2}=5x-10 \\ \\ 13x-53=10x-20 \\ \\ 3x-53=-20 \\ \\ 3x=33 \\ \\ \boxed{x=11} \\ \\ m\angle RDB=5(11)-10=\boxed{45^{\circ}}[/tex]

The measure of the angle ∠RDB will be 45°.

In geometry, a chord of a circle is a straight line segment whose endpoints both lie on the circle. A diameter of a circle is the longest chord, and it passes through the centre of the circle.

Calculate the value of x as below,

( 13x + 7 - 60 ) / 2 = 5x - 10

13x - 53 = 10x - 20

3x - 53 = -20

3x = 33

x = 11

The measure of the angle ∠RDB is,

∠RDB = 5x - 10

∠RDB = ( 5 x 11 ) - 10

∠RDB = 45°

Therefore, the value of an angle ∠RDB will be 45°.

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Answer:

2.475

Step-by-step explanation:

Answer:

2.475

Step-by-step explanation:

Could you please give me brainliest for this? Thanks!

The number of ways that 7 new members be chosen if 2 or fewer must be from the Senior class is; 705 ways

The formula for probability combination is;

nCr = n!/(r! * (n – r)!)

where;

n is the total number of items.

r is the number of things that may be selected at one time.

The number of ways that 2 students can be selected from the senior class is;

N(2 students from the SR class) = 3C2 * 10C2 = 135 ways

Similarly;

N(1 student from the SR class) = 3C1 * 10C3 = 360

N(0 students from the SR class) = 3C0 * 10C4 = 210

Thus, number of ways that 7 new members be chosen if 2 or fewer must be from the Senior class is;

135 + 360 + 210 = 705 ways

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Answer:

4

20

40

Step-by-step explanation:

Since the final line says 8 x 5, I know that the final answer is 40.

That means that the blank on the first line has to be 4

The second line is missing a 20 because 20 + 20 = 40

Answer: There are multiple answers.

Step-by-step explanation: To find x...simply ad together what you have (The numbers given) and subtract from 180.

(I did this a while ago, don't take my word  for it)

The division between 756 and 26 can be represented as a fraction or decimal as 378/13 or 29.1 respectively

Fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

We can say the fraction of a number is a ratio between the numerator and denominator of two numbers.

Fractions are often as a result of dividing two numbers and they probably don't give a whole number.

In this case, the division between 756 and 26 will result in a fraction because both numbers are not completely divisible by one another.

To divide 756 by 26;

756 ÷ 26 =

Divide both sides by 2

756 ÷ 26 = 378 / 13

Both numbers are not divisible by one another from here, but we can represent this as a fraction of one another;

756 ÷ 26 = 29.076923

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The solution for x in the inequality is x ≥ 343

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

412≤1.2x

Divide both sides of the inequality by 1.2

So, we have

412/1.2 ≤ 1.2x/1.2

Evaluate the quotients

343 ≤ x

Rewrite the expression as

x ≥ 343

Hence, the solution is x ≥ 343

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Step-by-step explanation:

15 e^(4x) =12

divide both sides by 15

e^(4x) = 0.8

if e^y = X

then y = ln x

4x=ln 0.8

4x=-0.22314

dividing both sides by 4

4x/4= -0.22314/4

x = -0.0558

Answer: 8 fields are needed

Step-by-step explanation:

65 ÷ 9 = 7.222
You can't have a partial field, so you round up to find the number of fields for all 65 cows.
8 fields will fit 65 cows

Answer: 8

Step-by-step explanation:

you divide 65 by 9 but you cant have 7.222 cows so its 8

Answer:[tex]26\frac{7}{12}[/tex]

Step-by-step explanation:

2 1/5 * 12 1/2 = 319/12

319/12 = [tex]26\frac{7}{12}[/tex]

Answer:

1

Step-by-step explanation:

[tex]f(2)[/tex] is equal to the [tex]y[/tex] coordinate of the point on the graph of the function with [tex]x[/tex] coordinate 2.

Answer:

Sydney will have to pay -5, and her brother will have to pay -7. Her brother will have to pay $2 more than Sydney.

Step-by-step explanation:

The statement that best describes the functions represented in the graphs is B. Only function p is continuous and linear.

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

A function at a place can only be continuous if it is defined there, has a limit there, and its value at that point is equal to the value of the limit there.

The graph of function p is linear and continuous

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Answer:is 1

identity property of 0 the definition is adding 0 to any number results in the number itself. and one 1 is have the same but other 3 is not.

The correlation coefficient between Exam 1 scores and Exam 2 scores is given as follows:

0.8452.

The equation for this problem is given as follows:

b = r x Sy/Sx.

The variables of the equation are given as follows:

The input and the output variables in this problem are given as follows:

Hence the values of the parameters are given as follows:

b = 0.51, Sx = 11.6, Sy = 7.

Hence the numeric value of the correlation coefficient is obtained as follows:

b = r x Sy/Sx.

r x 7/11.6 = 0.51

0.6034r = 0.51

r = 0.51/0.6034

r = 0.8452.

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Hence, the probability of selecting two Democrats is [tex]45[/tex].

What is the probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen.

The meaning of probability is basically the extent to which something is likely to happen.

Here given that,

Consider a political discussion group consisting of [tex]9[/tex] ​Democrats, [tex]9[/tex] ​Republicans, and [tex]5[/tex] Independents. Suppose that two group members are randomly​ selected, in​ succession, to attend a political convention.

Let us assume ,

The discussion of the democratic is [tex]x_1=9[/tex].

The discussion of the democratic is [tex]x_2=9[/tex].

The discussion of the democratic is [tex]x_3=5[/tex]

So, the total number of candidates are

[tex]x_t=x_1+x_+x_3\\\\=9+9+5\\\\=23[/tex]

Probability of independate candidate from the group of candidates is

[tex]P_1=\frac{x_3}{x_t}\\\\P_1=\frac{5}{23}\\\\[/tex]

As, the remaining number of candidates after the selectio of the independent candidate is

[tex]x_r=x_t-1\\\\x_r=23-1\\\\x_r=22[/tex]

Now, the remaining number of candidates from the group of total remaining candidates is

[tex]P_2=\frac{x_1}{x_r}\\\\P_2=\frac{9}{22}[/tex]

So, the probability of an independent Democrat using the probability is

[tex]P=P_1[/tex] × [tex]P_2[/tex]

[tex]P=\frac{5}{23}[/tex] ×[tex]\frac{9}{22}[/tex]

[tex]P=\frac{110(207)}{506}\\\\P=\frac{22770}{506}\\\\P=45[/tex]

Hence, the probability of selecting two Democrats is [tex]45[/tex].

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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.

The total amount spent on the ingredients is

80x + 30y + 5z

Where x is the amount of flour, y is the amount of tomatoes and z is the cost of Mozzarella per kg.

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,

Ingredients    Amount       Cost per kg

Flour               x                   $80

Tomatoes       y                   $30

Mozzarella      5                    $z

The total amount spent on the ingredients can be given by the expression.

= 80x + 30y + 5z

Where x is the amount of flour, y is the amount of tomatoes and z is the cost of Mozzarella per kg.

Thus,

The total amount spent on the ingredients is

80x + 30y + 5z

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Answer:

C=0.8x+3.3y+0.5z

Step-by-step explanation:

khan

you`re welcome :)

Answer:

[tex]\huge\boxed{\sf 48r\² + 40r}[/tex]

Step-by-step explanation:

= -4r(-15r + 3r - 10)

Add -15r and 3r

= -4r(-12r - 10)

Distribute

= (-4r)(-12r) - (-4r)(10)

= 48r² - (-40r)

[tex]\rule[225]{225}{2}[/tex]

$105

Earnings for 1 hour=165÷11=$15

Earnings for 7 hours=15×7=$105

The profit function is P(x) = −0.5x² + 40x - 100

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

Cost function, C(x) = 50x + 100

Revenue function, R(x) = −0.5(x − 90)² + 4050

The profit function is the difference between the revenue and the cost

So, we have

P(x) = R(x) -CP(x)

Substitute the known values in the above equation, so, we have the following representation

P(x) = −0.5(x − 90)² + 4050 - 50x - 100

Evaluate the like terms

P(x) = −0.5(x − 90)² - 50x   + 3950

Expand

P(x) = −0.5(x² − 180x + 8100) - 50x   + 3950

Expand

P(x) = −0.5x² + 90x - 4050 - 50x   + 3950

Evaluate the like terms

P(x) = −0.5x² + 40x - 100

In (a), we have

P(x) = −0.5x² + 40x - 100

Using a graphing calculator, the reasonable domain is

3 < x < 75

So, the domain is 3 < x < 75

Here, we have

x = 40 or 50

So, we have

P(40) = -0.5(40)² + 40(40) - 100 = 700

P(50) = -0.5(50)² + 40(50) - 100 = 650

In (d), we have

P(40) = 700

P(50) = 650

This means that the profit reduces as they produce more

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Answer:

(0,-7)

Step-by-step explanation:

Plug in the X and Y's from the answer choices to get your answer. If the left of the equation (Y) is less than the right side (-1/2x - 6) it is correct!

Hope this helps!

The break-even point under the old situation is 680000, the break-even point under the proposed situation is 806451 and the birr sales volume must be obtained under the proposed plan to make as much profit as last year is 1129032.

In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total income are equal, or "even." Although opportunity costs have been paid and capital has obtained the risk-adjusted, projected return, there is no net loss or gain, and one has "broken even."

In the given question, last year sales=  birr 100000

net profit= 8% of sales

Fixed costs= birr 170000

Estimated sales increase= 25%

Estimated net profit= birr 30000

Increase in fixed cost due to moving to low-rent warehouse= birr 30000

(a) The break-even point under the old situation (X):

   = 100,000 * a - 170,000

   =1,000,000 * 8%

   a= 25% (net profit)

   X*a= 1170,000

   X=680,000

   That is, the break-even point under the old situation is 680000.

(b) The break-even point under the proposed situation is:

      = 1,250,000 x b - 170,000- 30,000

      = 80,000 + 30,000

      b= 24.8%

      X*b=200,00

      X=806451

      The break-even point under the proposed situation is 806451 and

(c) The birr sales volume must be obtained under the proposed plan to make as much profit as last year is:

        X*b -200,000= 80,000

        X*b = 280,00

        X= 1,129,032

The birr sales volume must be obtained under the proposed plan to make as much profit as last year is 1129032.

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Answer:

283 cm^2

Step-by-step explanation:

hi your welcome

Answer:

Step-by-step explanation:

radius = r = 17

height = h = 13

First calculate the total surface area =

2πr (r + h)

2 (3.14) 17 (17 + 13)

2 (3.14) 17 (30)

6.28 (17)(30)

106.76 (30)

3202.80  cm²

Then subtract the area of the bottom base of the cake:

Base of the cake is the area of the round base

π r² = 3.14 (17)²

3.14 (289) = 907.46 cm²

Subtract area of base from total surface area:

I am rounding:

3203 - 908 = 2295 cm²

Second option or B

Answer:

Plane PQY

Step-by-step explanation:

A plane is defined by 3 non-linear points. This is because if 3 linear points are given, only a line has been defined; its plane could be at any angle. The only answer choice that has non-linear points is PQY.

The total distance covered is 15000 m. The total time taken is 5220 seconds and the speed is 2.87 m/s.

We know that speed has to do with the ratio of the distance that has been covered to the time taken. The speed is a scalar quantity and as such we do not consider the direction hence we would not consider that going back in the opposite direction. The total distance can be obtained algebraically.

The total distance that the student travelled can be obtained from;

5000 m + 5000 m + 5000 m

= 15000 m

The total time taken in seconds = 1800 seconds + 1800 seconds + 1620 seconds

= 5220 second

Speed = Distance/ Time

= 15000 m/5220 second

= 2.87 m/s

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