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Step-by-step explanation:

Let take the first derivative

[tex] \frac{d}{dx} ln(x)) = x {}^{ - 1} [/tex]

The second derivative

[tex] - {x}^{ - 2} [/tex]

The third derivative

[tex]2 {x}^{ - 3} [/tex]

The fourth derivative

[tex] - 6 {x}^{ - 4} [/tex]

The fifth derivative

[tex]24 {x}^{ - 5} [/tex]

Let create a pattern,

The values always have x in it so

our nth derivative will have x in it.

The nth derivative matches the negative nth power so the nth derivative so far is

[tex] {x}^{ - n} [/tex]

Next, lok at the constants. They follow a pattern of 1,2,6,24,120). This is a factorial pattern because

1!=1

2!=2

3!=6

4!=24

5!=120 and so on. Notice how the nth derivative has the constant of the factorial of the precessor

so our constant are

[tex](n - 1)[/tex]

So far, our nth derivative is

[tex](n - 1)!x {}^{ - n} [/tex]

Finally, notice for the odd derivatives we are Positve and for the even ones, we are negative, this means we are raised -1^(n-1)

[tex] - 1 {}^{n -1} (n - 1) ! {x}^{-n} [/tex]

That is our nth derivative

Answer:

y = - 2x - 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, - 4) ← 2 points on the line

m = [tex]\frac{-4-0}{0-(-2)}[/tex] = [tex]\frac{-4}{0+2}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2

the line crosses the y- axis at (0, - 4 ) ⇒ c = - 4

y = - 2x - 4 ← equation of line

Answer:

45 meters

Step-by-step explanation:

[tex]Area=\frac{1}{2}bh\\ A=\frac{1}{2}(6)(15)\\ A=3(15)\\A=45[/tex]

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Answer:

A=45 m²

Step-by-step explanation:

The formula for the area of a triangle is, [tex]\bigstar\underline{\boxed{\sf{A=\frac{bh}{2}}}}[/tex].

where :

[tex]\triangleright\sf{A=Area,b=base,h=height}\triangleleft[/tex]

Substitute the values,

[tex]\large\begin{gathered}\sf{A=\frac{6*15}{2} \\ \sf{A=\frac{90}{2}\\\bigstar\underline{\boxed{\sf{A=45 \ m^2}}}} \end{gathered}[/tex]

Done !! Hope this made sense to you :)

[tex]\small\boldsymbol{Calligraphy}[/tex]

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Answer: I don't know what you are talking about, but if x is the area, then the answer is 1,210.

Step-by-step explanation: 44 x 55 x 1/2 = 1,210. The formula for the area of a triangle is 1/2 times length times height. Therefore, x = 1,210

Hope this helps.

Answer:

$31,341.81

Step-by-step explanation:

The compound amount equation is A = P(1 + r/n)^(nt), where P is the unknown principal, r is the annual interest rate, n is the number of compounding periods per year and t is the number of years.  We want to solve this for P:

       A

------------------- = P

(1 + r/n)^(nt)

Substituting the given numerical values;

     $45,000

 ---------------------------  =  P

   (1+0.073/4)^(4*5)

Using a calculator, we evaluate this expression, obtaining:  $31,341.81

Answer:

The equation of the line passing through the points (3,7) and (-2,5) is y=⅖x+29/5

Step-by-step explanation:

Greetings !

[tex]first \: find \: the \: slope \: m \\ m = \frac{(Y₂-Y₁)}{(X₂-X₁)} ..substitute \: vlues \\ m = \frac{(5 - 7)}{( - 2 - 3)} = \frac{ - 2}{ - 5} = \frac{2}{5} \\ y = mx + b \: to \: find \: equation \: of \: aline \\ between \: two \: poins and \: use \: \\ one \: of \: the \: two \: points \: lets \: take( - 2.5) \\ y = mx + b \\ 5 = \frac{ - 2}{5} ( - 2) + b \\ 5 = \frac{ - 4}{5} + b \\ 5 + { - 4}^{5} = b \\ \frac{25 + 4}{5} = b \\ b = \frac{29}{5} \\ finally \: equation \: of \: the \: line \: will \: be \\ y = \frac{2}{5} x + \frac{29}{5} [/tex]

Using the normal distribution, it is found that 0.4068 of crocodiles live between 17.5 and 20.5 years.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given as follows:

[tex]\mu = 18, \sigma = 2.6[/tex]

The proportion of crocodiles live between 17.5 and 20.5 years is the p-value of Z when X = 20.5 subtracted by the p-value of Z when X = 17.5, hence:

X = 20.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{20.5 - 18}{2.6}[/tex]

Z = 0.96

Z = 0.96 has a p-value of 0.8315.

X = 17.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{17.5 - 18}{2.6}[/tex]

Z = -0.19

Z = -0.19 has a p-value of 0.4247.

0.8315 - 0.4247 = 0.4068

0.4068 of crocodiles live between 17.5 and 20.5 years.

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The probability that a person chosen at random have run a red light in the past year is 0.45.

Given that 150 people have responded yes and 185 have responded no in a group of people when they asked whether they have run a red light.

Probability lies between 0 and 1. The value of probability can be find by :

Probability= Number items/total items.

Number of people who said that they have run red light=150

Number of people who said that they have not run red light=185

Total people=150+185

=335 people

Probability that a person chosen at random have run red light in the past year=

=Number of people who said that they have run red lights / total people

=150/335

=0.447

After rounding off it will be 0.45.

Hence the probability that a person chosen at random have run a red light in the past year is 0.45.

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Answer:

a=0

Step-by-step explanation:

If this is what you are asking, and if I understand it correctly, 8*8=64 and not 8, but 8*0=0, therefore 0 is a solution.

Answer:

  8

Step-by-step explanation:

The definition of an average can be used with the given values to write an equation for the number of boys.

The average is the total divided by the number. If there were n original boys, the total was T, where ...

  T/n = 145   ⇒   T = 145n

Adding two boys with an average of 160 cm height, the new total became (T +2(160)) and the new average became ...

  (T +2(160))/(n +2) = 148   ⇒   T = 148(n +2) -320

Equating the values of T, we have ...

  T = 145n = 148(n +2) -320

Solving for n, we find ...

  0 = 3n -24 . . . . . . . . . . . . subtract 145n and simplify

  0 = n -8 . . . . . . . . . . . divide by 3

  8 = n . . . . . . . . . . . add 8

The number of boys in the group at first was 8.

Answer: B is dependent and M is independent

Step-by-step explanation:

This is because the question says that they are raising money to buy books. In order to buy the books, they must raise money. So they raise money than buy the books which makes buying the books dependent on how much they raise.

Answer: The largest common factor of 28 and 32 is 4.

Step-by-step explanation:

The factors of 28 are 1, 2, 4, 7, 14, 28

The factors of 32 are 1, 2, 4, 8, 16, 32

The measure of the indicated angle to the nearest degrees is 23 degrees.

The angle of a right angle triangle can be found as follows:

Therefore, the angle can be found using trigonometric ratios as follows;

cos ∅ = adjacent / hypotenuse

Therefore,

adjacent side = 35 units

hypotenuse side = 38 units

Hence,

cos ∅ = 35 / 38

∅ = cos⁻¹ 0.92105263157

∅ = 22.9272842944

∅ ≈ 23 degrees.

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The equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6

From the given table, we see that the x-intercepts are;

(-3, 0), (1, 0) and (2, 0)

Now, we are told the the x-intercepts have a multiplicity of one which means they occur as roots only once. Thus, we can say that the roots in factor form are;

(x + 3), (x - 1), (x - 2)

Then, the polynomial will be;

h(x) = (x + 3) * (x - 1) * (x - 2)

h(x) = (x + 3)(x² - 3x + 2)

h(x) = x³ + 3x² - 3x² - 9x + 2x + 6

h(x) = x³ - 7x + 6

Thus, the equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6

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The two-column proof that proves that ∠O ≅ ∠R using the SSS and CPCTC theorems is shown in the image attached below.

The side-side-side congruence theorem (SSS) states that when three sides of a triangle are congruent to the corresponding three sides of another triangle, then both triangles are considered congruent to each other.

The CPCTC theorem states that when two triangles are proven to be congruent by any triangle congruent theorem, then all the corresponding parts of the congruent triangle are congruent. This implies that the corresponding sides and angles of both triangle are equal or congruent.

We are asked to prove that ∠O ≅ ∠R.

With the given image, we would draw segment UP. Thus, based on the reflexive property, UP ≅ UP (one pair of congruent sides).

We are given two pairs of corresponding sides already, which are: UO ≅ UR and PO ≅ PR.

This means that triangles OUP and RUP have three pairs of corresponding congruent sides. Therefore, ΔOUP ≅ ΔRUP.

Applying the CPCTC theorem, ∠O ≅ ∠R.

The two-column proof is attached in the image below.

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Answer:

Step-by-step explanation:

SOLUTION :

let total people in the party be x i.e. 1260

then , number of men = 5/9 of x

= 5/9 of 1260 = 5 × 140 = 700 men

now ,

number of women = Total person - (number of total men)

= ( 1260 - 700 ) women

= 560 women

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Considering the given equations for revenue and cost, the company will break-even when 356 widgets are sold.

The break-even point is the value of x for which:

R(x) = C(x).

In this problem, the functions are:

Hence:

R(x) = C(x)

16x = 12x + 1424

4x = 1424

x = 1424/4

x = 356

The company will break-even when 356 widgets are sold.

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Given the diameter of the circular garden, the area of the garden is 28.36 yd².

The area of a circle is expressed as; A = πr²

Given that;

A = πr²

A = 3.14 × (3yd)²

A = 3.14 × 9yd²

A = 28.36 yd²

Given the diameter of the circular garden, the area of the garden is 28.36 yd².

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Answer:

$1800

Step-by-step explanation:

Volume of the foundation: 30*12*6 = 2160 cubic feet

we need to convert this into yards because a truckload is 8 cubic yards, 2160/3 = 720 cubic yd

One truckload is 8 cubic yards

# of truckloads needed: 720/8 = 90 truckloads

Cost: $20*90 = $1800

Answer:

6

Step-by-step explanation:

The equation for this problem would be c = (20 + 8) / 2 - 8. Add 20 and 8 to get 28, divide 28 by 2 to get 14, then subtract 8 to get 6.

The diameter of the circle is 11.8 units

The circle equation is given as:

(x - 2)^2 + (y + 6)^2 = 35

A circle equation is represented as:

(x - a)^2 + (y - b)^2 = r^2

Where

Diameter = 2r

By comparing both equations, we have

r^2 = 35

Take the square root of both sides

r = 5.9

Multiply by 2

2r = 11.8

Hence, the diameter of the circle is 11.8 units

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Answer:

Second option

Step-by-step explanation:

As its a solid line, it indicates the inequality contains equal to in it. As the line crosses the x - axis it must be an option whereby x > or x < . Now read the value which is 7 therefore x ≤ 7

Using the z-distribution, the p-value would be given as follows:

b) 0.0086.

At the null hypothesis we test if the means are equal, hence:

[tex]H_0: \mu_D - \mu_C = 0[/tex]

At the alternative hypothesis, it is tested if they are different, hence:

[tex]H_1: \mu_D - \mu_C \neq 0[/tex]

For each sample, they are given as follows:

Hence, for the distribution of differences, they are given by:

The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Hence:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

[tex]z = \frac{-2 - 0}{0.76}[/tex]

z = -2.63.

Using a z-distribution calculator, for a two-tailed test, with z = -2.63, the p-value is of 0.0086.

Hence option B is correct.

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The total repayment made, including principal and interest is $1262.27

The formula for calculating the compound interest is calculated as shown below;

A = P(1+r)^t

where

P is the principal = $1100

rate = 3.5% = 0.035

time "t" =4 years

Substitute

A. = 1100(1+0.035)^4
A = 1100(1.035)^4
A = 1100(1.14752)

A = 1262.27

Hence the total repayment made, including principal and interest is $1262.27

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Answer:

[tex]15x^3 +10x^2 - 15x[/tex]

Step-by-step explanation:

Hello!

Use the distributive property and multiply like terms.

The simplified form is [tex]15x^3 +10x^2 - 15x[/tex].

Answer: the speed of the stream is 9mph

Answer:

0

Step-by-step explanation:

8z +12 = 12

8z = 0

z =0

Answer:

The answer is 0

Step-by-step explanation:

4(2z+3)=12?=

We use the distributive property to distribute the 4 into the 2.

8z=3=12?=

8 + 3 is 12 so the z has no part to play in this.

z=0

You could also have divided from both sides of the equation, but doing it this way is easier for me.

Answer:

the ansqer is g(x) = 4^x-4 + 2