Differentiate the function with respect to x.

On differentiating the given function with respect to x , we get f'(x) = 10x⁴ - 8x⁻⁵  .

In the question ,

it is given that

the function is f(x) = 2x⁵ + 3 + 2x⁻⁴

the derivative of x⁵ is [tex]=[/tex] 5x⁴ ,

the derivative of 3 is = 0

the derivative of x⁻⁴ = -4x⁻⁵ .

on differentiating the function  f(x) = 2x⁵ + 3 + 2x⁻⁴ with respect to x is

f'(x) = 2*d/dx(x⁵) + d/dx(3) + d/dx(x⁻⁴)

Substituting the values of derivative ,

we get

f'(x) = 2*(5x⁴) + 0 + 2(-4x⁻⁵)

f'(x) = 10x⁴ - 8x⁻⁵

Therefore , On differentiating the given function with respect to x , we get f'(x) = 10x⁴ - 8x⁻⁵  .

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The probability that the Yankees will win when they score fewer than 5 runs is; 0.567

We are given;

Event A which is when Yankees win has a probability of; P(A) = -.45

Thus, Event that the Yankees don't win which is when they lose is;

P(A') = 1 - 0.45 = 0.55

Event B which is the event that the Yankees score 5 or more runs has a probability of; P(B) = 0.6

Event that the Yankees score 4 or less run is given by the probability;

P(B') = 1 - 0.6 = 0.4

The probability that the Yankees win and score 5 or more runs is;

P(A' ∩ B') = 0.34

Thus, the probability that the Yankees will win when they score fewer than 5 runs wanted is given by the chain rule in conditional probability of the formula;

P(A' | B') = P(A' ∩ B')/P(B') = 0.34/0.6

P(A' | B') = 0.567

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Answer:

$ 52.63

Step-by-step explanation:

The brand C detergent has the best value.

The mathematical branch known as arithmetic deals with the study and application of numbers, their relationships, and mathematical observations.

As per the given data in the question:

The information regarding the quantity and cost of 3 detergents is given in the question.

We have to find out which detergent is the most economical.

The detergent with the lowest cost/quantity will be the most economical.

For Brand A

Cost = $14.99

Quantity = 40 ounces

cost/quantity = 14.99/40 = 0.374 dollar/ounce

For Brand B

Cost = $19.99

Quantity = 50 ounces

cost/quantity = 19.99/50 = 0.399 dollar/ounce

For Brand C

Cost = $21.99

Quantity = 1/2 gallon = 64 ounces

cost/quantity = 21.99/64 = 0.343 dollar/ounce

The brand C detergent has the best value.

Hence, The brand C detergent has the best value.

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The correct statement:  

1/3 equal to 4/12; 4/6 equal to 2/3; 2/5 equal to 5/10

incorrect statement:  2/5 equal to 1/3

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

a) 4/12

Writing into Simplest form

4/12 = 1/3

b) 4/6

Writing into Simplest form

4/6 = 2/3

c) 2/5 cannot be simplified to 1/5

d) 5/10

Writing into Simplest form

5/10= 1/2

Hence, The correct statement:  1/3 equal to 4/12; 4/6 equal to 2/3; 2/5 equal to 5/10 and incorrect statement:  2/5 equal to 1/3.

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Answer:

Step-by-step explanation:

2x(x + 7)(x²+49) = 0

(apply the zero product)

x=0 or x+7 =0 or x² + 49 = 0

x+7 =0

x=-7

x² + 49 = 0

no real solution for this i think

Answer = x=0 or x=-7

solution

3x+18/18

ans4

A) The data modelling is an exponential function.

B) The explicit funciton that will be used to represent the data is;

f(n) = 2(2)^(n - 1)

C) The average rate of change here is; 7

A) We are given the coordinates as;

(1, 2), (2, 4), (3, 8), (4, 16)

From the given coordinates, we can observe a pattern which is that when x increases by 1, then y is multiplied by 2.

Thus, we can see that as the quotient between consecutive terms is the same, the data is a geometric sequence which is an exponential function.

B) The explicit formula that will be used for a geometric sequence with common ratio r and first term a is given by:

f(n) = ar^(n - 1)

Since first term ; a = 2

and common ratio r = 2, then we can say that;

f(n) = 2(2)^(n - 1)

C) The formula for average rate of change here is;

dy/dx = (y₂ - y₁)/(x₂ - x₁)

The coordinates of the 2nd and 4th day are;

(2, 4) and (4, 16)

Thus;

dy/dx = (16 - 4)/(4 - 2)

dy/dx = 14/2 = 7

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Answer:

[tex]3x - 10 = 25 + x + 15[/tex]

according to theorem

[tex]3x - x = 40 + 10 \\ 2x = 50 \\ x = 25[/tex]

Hopefully this will help u

Step-by-step explanation:

first order them from least to greatest

13,14,18,21,22,26,32,39,39,42

then just look for the term in the middle

sunset there are 2 numbers in the middle you will add them both and subtract them by 2

42+39 then / 2 =40.5

Answer:

p=p=10/3

Explanation:

9-6p =-11=p=10/3

Quadratic equation that passes through the points (-4,2) and (1,2) and a form a graph of horizontal line y =2.

Graph is attached.

As given in the question,

Quadratic equation passes through the points (-4,2) and (1,2)

(x₁, y₁) =(-4,2)

(x₂ ,y₂) = (1,2)

(y-y₁)/ (x-x₁) = (y₂ -y₁)/(x₂ -x₁)

⇒(y-2)/(x +4) =(2-2)/)1+4)

⇒ (y-2)/(x+4) =0

⇒y -2 =0

⇒y =2

Quadratic equation formed from the given points (-4,2) and (1,2) is y =2.

which represents the horizontal line and does not have any vertex.

Graph of the quadratic equation y =2 is attached.

Therefore, quadratic equation that passes through the points (-4,2) and (1,2) and a form a graph of horizontal line y =2.

Graph is attached.

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Answer:

x = 62

Step-by-step explanation:

40 + (x + 16) + x = 180 (sum of angles in a triangle=180)

2x + 56 = 180

2x = 124

x = 62

The value of 2*(3*5) = 68.

The value of (2*3)*5 = 68.

What is multiplication?

A mathematical formula that specifies the objects to be multiplied, known as a factor, produces a product. For instance, the product of 6 and 5 is 30.

Given: The operation * is defined as,

a*b = a + b - 2ab

We have to find the value of 2*(3*5) and (2*3)*5

First to find the value of 2*(3*5).

2*(3*5) = 2*(3 + 5 - 30) = 2*(-22) = 2 + (-22) - 2(-22)(2) = 68.

Now to find the value of (2*3)*5.

(2*3)*5 = (2 + 3 - 12)*5 = -7*5 = (-7) + 5 - 2(-7)(5) = -2 + 70 = 68.

Therefore, 2* (3*5) = 68 and (2*3)*5 = 68.

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The simple interest on a $10000 loan offered at a rate of 9% over 240 days is $10591.78

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

The formula is given as

S.I = p(1 + rt)

Substituting the values into the equation,

S.I = 10000(1 + 0.09 * 240)

S.I = 10591.78

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The value of pH of the coffee is 4.89

pH is a measure of hydrogen ion concentration, a measure of the acidity or alkalinity of a solution

Given:  The formula pH= -log₁₀ C,

where is the concentration of hydronium ions in the solution measured in moles per litre

The concentration(C) of Hydronium ions type of coffee is 1.3 x 10⁻⁵ moles per liter

To calculate the pH, we will substitute the value of the concentration (C) into the given formula:

pH= -log₁₀ C                     (C = 1.3 x 10⁻⁵ moles per liter)

pH = -log₁₀(1.3 x 10⁻⁵) = 4.89

Therefore, the pH of the coffee is 4.89

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The equation of the transformation of the exponential function y = 2ˣ in the form y = A·2ˣ + k, obtained from the simultaneous found using the points on the graph is y = (-2)·2ˣ + 3

An exponential equation is an equation that has exponents that consists of variables.

The given equation is y = 2ˣ

The equation for the transformation is; y = A·2ˣ + k

The points on the graphs are;

(0, 1), (1, -1) and (2, -5)

Plugging the x and y-values to find the value A and k gives  the following simultaneous equations;

When x = 0, y = 1, therefore;

1 = A·2⁰ + k = A + k

1 = A + k...(1)

When x = 1, y = -1, which gives;

-1 = A·2¹ + k

-1 = 2·A + k...(2)

Subtracting equation (1) from equation (2) gives;

-1 - 1 = 2·A - A + k - k

-2 = A

1 = A + k, therefore;

1 = -2 + k

k = 2 + 1 = 3

k = 3

Which gives;

y = -2·2ˣ + 3 = 3 - 2·2ˣ

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Tony has 10.5 cookies.

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order term, where m is the slope and b is the y-intercept.

Given that, Adam has 6 cookies less than Tony, there are a total of 15 cookies between both of them.

Let the number of cookies Tony has be x,

x+x-6 = 15

2x - 6 = 15

2x = 21

x = 21/2 = 10.5

Hence, Tony has 10.5 cookies.

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The interest eared from the given amount, rate of interest and time period is $426.883.

Given that, amount = $700, rate of interest = 4% and time period = 2 years.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest is [tex]Amount=Principal(1+\frac{r}{100})^{nt}[/tex]

Let the money deposited be x.

So, [tex]700=x(1+\frac{4}{100} )^{2\times12}[/tex]

⇒ [tex]700=x(1+0.04)^{24}[/tex]

⇒ [tex]700=x(1.04)^{24}[/tex]

⇒ 700 = 2.563x

⇒ x=700/2.563

⇒ x=$273.117

So, interest = 700-273.117

= $426.883

Therefore, the interest eared from the given amount, rate of interest and time period is $426.883.

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By using the concept of linear inequation, the required solution is

[tex]x > \frac{5}{3} \ or \ x < -\frac{50}{3}[/tex]

What is linear inequation?

Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by [tex]> , < . \geq, \leq[/tex]

A one degree inequation is known as linear inequation.

Here the given linear inequation is

[tex]3x \geq 5 \ or \ \frac{-3}{5}x -3 > 7[/tex]

Now

[tex]3x \geq 5 \ or \ \frac{-3}{5}x -3 > 7\\\\x \geq \frac{5}{3} \ or \ \frac{-3}{5} x > 7 + 3\\\\x \geq \frac{5}{3} \ or \ \frac{-3}{5}x > 10\\\\x > \frac{5}{3} \ or \ x < \frac{10 \times 5}{-3}\\\\x > \frac{5}{3} \ or \ x < -\frac{50}{3}[/tex]

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The box must be added with 7 cubic feet of sand

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also be defined as the capacity of an object.

It is measured in cubic units.

The volume of a box is length × width × height

represent the original length, width and height by x ,y ,z respectively

This shows that the volume of the original box= x× y× z = 1cubic foot

when the original length, width and height are doubled to give the new dimensions

Therefore the new length,width and height will be 2x, 2y and 2z

the volume of the new formed box = 2x×2y×2z

= 8xyz

XYZ= 1cubic foot

therefore 8xyz = 8cubic feet

since there is 1 cubic foot of sand in the box already,

then( 8-1)cubic feet = 7cubic feet will be added.

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Answer:

a) about 190 acres

b) around 240 acres

c) exponential decay because the amount of land available is decreasing at an increasingly rapid rate over time.

Answer:

Step-by-step explanation:

i think the answer is 10 or 5

The width of the river to the nearest foot will be 45 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Paula remains on a waterway and sights the contrary bank at a point of the wretchedness of 7 degrees.

If Paula is 5.5 feet tall.

Let 'w' be the width of the river. Then the width of the river will be given as,

tan 7° = 5.5 / w

0.12278 = 5.5 / w

w = 44.79

w ≈ 45 feet

The width of the river to the nearest foot will be 45 feet.

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Answer:

C

Step-by-step explanation:

Even though quotient means divide I instead used the minus symbol since they both mean something negative or taking away. Then, the 7 goes before everything adding onto what was left from the second part.

The total amount he will pay after 25 years is $18,97,500.

His monthly payment will be $6,325.

Given, the cost of mortgage is $720,000, and the owner of the house makes a down payment of $60,000, with 7.5% interest rate and 25 years repayment plan.

Now, the total amount of the loan be,

720000 - 60000 = 660,000

monthly rate = 7.5/12 = 0.625%

Number of payment periods = 25

Total amount he has to pay after 25 years,

660000 + (660000×7.5×25)/100

= $18,97,500

His monthly payment will be

1897500/25×12

= $6,325

Hence, the total amount he will pay after 25 years is $18,97,500

also, his monthly payment will be $6,325.

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The  mean height of the low tides is 1.21 ft

The heights of the low tides for four days are -0.22 ft, 2.64 ft, -0.22 ft, and 2.64 ft

The mean of a sample is given by the formula =

summation of all observation / number of observation

mean = (x₁ + x₂ + x₃ + x₄)/ 4

mean = -0.22 + 2.64 - 0.22 + 2.64 / 4

mean = 4.48 / 4 = 1.21

Therefore, the  mean height of the low tides is 1.21 ft

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Answer: (4,-3)

Step-by-step explanation:

4x+5y=1       (1)

3x-2y=18     (2)

Multiply both parts of equation (1) by 2 and both parts of equation (2) by 5:

8x+10y=2

15x-10y=90

Sum these equations:

23x=92

Divide both parts of the equation by 23:

x=4

Substitute the value of x=4 into equation (1):

4(4)+5y=1

16+5y=1

16+5y-16=1-16

5y=-15

Divide both parts of the equation by 5:

y=-3

Thus, (4,-3)

Answer:  the correct answer is 150 minutes for 40 pages.

Step-by-step explanation:

It takes a word processor 45 minutes to word process and spell check 12 pages.

45 minutes / 12 pages = 3.75 minutes per page

3.75 min/page x 40 pages = 150 minutes

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Work Shown:

11 rock songs

229 total

11/229 is the probability of randomly selecting a rock song. The fraction doesn't reduce since 11 and 229 have no factors in common (other than 1).

If you wanted to convert to decimal form, then 11/229 = 0.04803 approximately. This converts to about 4.803%

Diving the polynomial expression f(m) = 8m^3 + 5m^2 - 32m - 20 and g(m)  = 8m + 5, as (f/g)(m) using long division gives m^2 - 4

Long division refers to a way of dividing large numbers including polynomials

performing the long division  (f/g)(m) gives

divisor               8m + 5

dividend            8m^3 + 5m^2 - 32m - 20                      

quotient            m^2

multiplication (quotient and divisor) = 8m^3 + 5m^2

subtraction (dividend - result of multiplication) =  - 32m - 20                       new dividend =  - 32m - 20

divisor               8m + 5

dividend           - 32m - 20                    

quotient            -4

multiplication (quotient and divisor) = - 32m - 20    

subtraction (dividend - result of multiplication) =  0               

new dividend = 0

The quotient is then added as

m^2 - 4

The second option is the correct option

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