What is the sum of the first 19 terms of the arithmetic series?

3+8+13+18+…



Enter your answer in the box.
_______

Answer:

a) The function is constantly increasing and is never decreasing

b) There is no local maximum or local minimum.

Step-by-step explanation:

To find the intervals of increasing and decreasing, we can start by finding the answers to part b, which is to find the local maximums and minimums. We do this by taking the derivatives of the equation.

f(x) = ln(x^4 + 27)

f'(x) = 1/(x^2 + 27)

Now we take the derivative and solve for zero to find the local max and mins.

f'(x) = 1/(x^2 + 27)

0 = 1/(x^2 + 27)

Since this function can never be equal to one, we know that there are no local maximums or minimums. This also lets us know that this function will constantly be increasing.

To find the interval of increase and decrease, we need to find where the derivative of the function is positive and negative, respectively. The derivative is positive when x > 0 and negative when x < 0.

To find the interval of increase and decrease, we need to find where the derivative of the function is positive and negative, respectively. The derivative of f(x) = ln(x^4 + 27) can be found using the chain rule: f'(x) = (4x^3)/(x^4 + 27).

The derivative is positive when (4x^3)/(x^4 + 27) > 0, which occurs when x > 0.

The derivative is negative when (4x^3)/(x^4 + 27) < 0, which occurs when x < 0.

Therefore, the interval of increase is (0, infinity) and the interval of decrease is (-infinity, 0).

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To compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values is poor, we use formulas for a binomial distribution. The mean is 78 and the standard deviation is 6.34. The interpretation of the mean is that for every 150 adults, the mean is the number of them that would be expected to believe that the overall state of moral values is poor.

To compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values is poor, we can use the formulas for a binomial distribution. The mean is found by multiplying the total number of trials (150) by the probability of success (0.52): mean = 150 × 0.52 = 78. The standard deviation is found by taking the square root of the product of the number of trials, the probability of success, and the probability of failure (1 - 0.52): standard deviation = √(150 × 0.52 × 0.48) = 6.34.

The interpretation of the mean is that for every 150 adults, the mean is the number of them that would be expected to believe that the overall state of moral values is poor, which in this case is 78.

It would not be unusual if 71 out of the 150 adults surveyed believe that the overall state of moral values is poor, as this value falls within one standard deviation from the mean.

Answer:

d = 50 in.

Step-by-step explanation:

A = Pi*r^2

625Pi = Pi*r^2

625 = r^2

r = 25 in

Diamenter = 2(radius=

d = 50 in

Best regards

Answer:

Long diagonal: 12.12 yd

Short diagonal: 7 yd.

Step-by-step explanation:

As you can see, 4 righ triangles are formed.

The larger diagonal divides the angle ∠AFM=60° into two angles of 30° each.

Then,  choose one the triangles that has the angles of 30°. The hypotenuse will be the side lenght of 7 yards, the long diagonal (D) will be twice the adjacent side and the short diagonal (d) will be twice the opposite side.

Then:

- Long diagonal:

[tex]\frac{D}{2}=7*cos(30\°)=6.06yd\\\\D=2(\frac{D}{2})=2(6.06yd)=12.12yd[/tex]

- Short diagonal:

[tex]\frac{d}{2}=7*sin(30\°)=3.5yd\\\\d=2(\frac{d}{2})=2(3.5yd)=7yd[/tex]

Answer:

The length of diagonals are 7 yd and 12.12 yd

Step-by-step explanation:

Let the point of intersection called as 'D'

<AFD = <MFD =60/2 = 30°

Then < AFM = <AFD + <MFD

Consider the ΔAFD

The angles are 30°, 60° and 90 then sides are in the ratio

1 : √3 : 2

The two diagonals are MA and FR

MA = MD + AD = 7/2 + 7/2 = 7 yd

FR = FD + RD =  7√3/2 +  7√3/2 =  7√3 = 12.12 yd

Therefore the length of diagonals are 7 yd and 12.12 yd

Rewrite y^4 as (y^2)^2

(y^2)^2 + 14y^2 +49

Rewrite 49 as 7^2

(y^2)^2 + 14y^2 +7^2

Factor using the perfect square rule.

Final answer: (y^2 + 7)^2

The factorization of given expression  [tex]y^{4}[/tex] + 14y² + 49 is a perfect square which is equal to (y² + 7)².

What is factorization ?

The factorization of algebraic expressions is the process of identifying two or more expressions whose product is the given expression.

The given expression is [tex]y^{4}[/tex] + 14y² + 49.

Before factorization if we look at the given expression we can find out that it is a form of perfect square which is :

A² + B² + 2AB.

Let's convert the given expression in the perfect square form. This will be equal to :

(y²)² + (7)² + 2 × y² × 7

We know that the expansion A² + B² + 2AB is equal to (A+B)².

Here ; A = y² and B = 7.

So , the factorization of given expression  [tex]y^{4}[/tex] + 14y² + 49 is equal to :

(y² + 7)²

Therefore , the factorization of given expression  [tex]y^{4}[/tex] + 14y² + 49 is a perfect square which is equal to (y² + 7)².

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Answer:

A. 5/9    B. 1/6.

Step-by-step explanation:

Total possible events = 6*6 = 36.

A.  The possible combinations for the sum  being <= 6 are:

1 ,1  2,2   3,3   1,2  1,3  1,4  1,5  2,1   2,3  2,4  3,1   3,2  3,3  4,1  4,2  5,1

= 16

So Probability of Sum > 6 =  (36-16) / 36

= 20/36

= 5/9.

B.   Possible combinations where the sum is divisible by 6  are

3,3  2,4  4,2  1,5  5,1. 6,6   =   6.

So the required probability =  6/36

= 1/6.

Answer:

The measure of the line segment GE is [tex]18\ units[/tex]

Step-by-step explanation:

we know that

The Intersecting Secant-Tangent Theorem , states that the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment

so

In this problem

[tex]GE*GF=GH^{2}[/tex]

substitute the values

[tex](8+x)(8)=12^{2}[/tex]

solve for x

[tex]8x+64=144[/tex]

[tex]8x=144-64[/tex]

[tex]8x=80[/tex]

[tex]x=10[/tex]

Find the measure of the line segment GE

[tex]GE=8+10=18\ units[/tex]

Answer:

[tex]\large\boxed{A=x^2+23x+49}[/tex]

Step-by-step explanation:

Subtract the area of a square (x + 1) × (x + 1)

from the area of a rectangle (x + 10) × (2x + 5)

The area of a square:

[tex]A_s=(x+1)(x+1)[/tex]            use FOIL: (a + b)(c + d) = ac + ad + bc + bd

[tex]A_s=(x)(x)+(x)(1)+(1)(x)+(1)(1)=x^2+x+x+1=x^2+2x+1[/tex]

The area of a rectangle:

[tex]A_r=(x+10)(2x+5)[/tex]              use FOIL

[tex]A_r=(x)(2x)+(x)(5)+(10)(2x)+(10)(5)=2x^2+5x+20x+50=2x^2+25x+50[/tex]

The area of a figure:

[tex]A=A_r-A_s[/tex]

Substitute:

[tex]A=(2x^2+25x+50)-(x^2+2x+1)=2x^2+25x+50-x^2-2x-1[/tex]

combine like terms

[tex]A=(2x^2-x^2)+(25x-2x)+(50-1)=x^2+23x+49[/tex]

Answer:

Step-by-step explanation:

There would be 216 outcomes because

6*6=36 outcomes so

6*6*6, or 36*6, = 216.

When 3 fair dice are rolled then there are 216 possible outcomes.

What is mean by Probability?

The term probability refers to the likelihood of an event occurring.

Given that;

When 2 fair dice are rolled there are 36 possible outcomes.

Now,

Since, When 2 fair dice are rolled then possible outcomes = 6 x 6 = 36

So, When 3 fair dice are rolled then possible outcomes = 6 x 6 x 6

                                                                                      = 216

Thus, When 3 fair dice are rolled then there are 216 possible outcomes.

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Answer:

An angle showing a turn through 1/5 of a circle is greater

Step-by-step explanation:

we know that

A complete circle represent [tex]360\°[/tex]

so

An angle showing a turn through 1/6 of a circle is

[tex](360\°)*(\frac{1}{6})=60\°[/tex]

An angle showing a turn through 1/5 of a circle is

[tex](360\°)*(\frac{1}{5})=72\°[/tex]

therefore

An angle showing a turn through 1/5 of a circle is greater

Answer:

r = - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The common ratio r of a geometric sequence is

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex] = .....

Hence

r = [tex]\frac{-52}{104}[/tex] = [tex]\frac{26}{-52}[/tex] = - [tex]\frac{1}{2}[/tex]

Final answer:

To find the volume of the soup can, one must use the formula for the volume of a cylinder, [tex]V = (pi)r^2h[/tex]. After substituting the given measurements, the calculated volume, rounded to the nearest tenth, is approximately 673.9 cubic centimeters.

Explanation:

The student asked about the volume of a cylindrical soup can with a given radius and height. To calculate this, the formula for the volume of a cylinder, which is V = \\(pi)r^2h, is used. Here, r represents the radius of the cylinder's base, and h represents the height of the cylinder. Substituting the given values into the formula, we get [tex]V = (pi)(4.3 cm)^2(11.6 cm)[/tex]. The calculated volume will give us the amount of space inside the soup can, measured in cubic centimeters (cm^3).

Step-by-step calculation:

Answer:

Step-by-step explanation:

The first triangle is a 30-60-90 right triangle.  We have a Pythagorean triple associated with this type of triangle that is

 (x , x√3, 2x) which represent the side lengths across from the

(30°, 60°, 90°)

We have the side length across from the 30° as 14.  That means that x = 14.  In our figure, "y" is across from the 60° which means that the side length is

14√3, which has a decimal equivalency of 24.24871131; in our figure "x" is the hypotenuse which is 14(2) which is 28.

For the intents and purposes of keeping you not confused:

x = 28, y = 14√3 (or 24.24871131)

The next triangle is also a right triangle but this one is a 45-45-90.  The Pythagorean triple for that triangle is

( x , x , x√2 ) as the side lengths across from the

(45°, 45°, 90°)

We have a side length across from the 90° as 18 units long; therefore, according to our Pythagorean triple:

x√2 = 18 and

x = [tex]\frac{18}{\sqrt{2} }[/tex] and, rationalizing the denominator:

[tex]x=\frac{18\sqrt{2} }{2}[/tex] so

x = 9√2, which has a decimal equivalency of 12.72792206.

Summing up again:

x = 9√2 (or 12.72792206)

ANSWER

[tex]A. \: \: y = 5x + \frac{3}{4} [/tex]

EXPLANATION

The slope-intercept form of an equation is given by;

[tex]y = mx + c[/tex]

wherever m is the slope and c is y-value of the y-intercept.

It was given that the slope is 5.

This implies that,

[tex] m = 5[/tex]

The y-intercept is

[tex](0, \frac{3}{4})[/tex]

This means that,

[tex]c = \frac{3}{4} [/tex]

We plug in the values to obtain,

[tex]y = 5x + \frac{3}{4} [/tex]

The correct choice is A.

Answer:

The volume of the similar prism is [tex]336\ cm^{3}[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

x----> the volume of the larger prism

y----> the volume of the smaller prism

so

[tex]z^{3}=\frac{x}{y}[/tex]

In this problem we have

[tex]z=2[/tex] -----> the scale factor

[tex]y=42\ cm^{3}[/tex]

substitute and solve for x

[tex]x=42(2^{3})=336\ cm^{3}[/tex]

Answer:

basketball hoop= 10 feet high

steve=5 feet tall

hes standing 12 feet away

so  i would say 3 feet away

The distance from the top of Steve's head to the hoop is 13 feet.

Given information in the question is the height of basketball hoop is 10 feet, height of Steve 5 feet and the distance from hoop to him is 12 feet.

Therefore the distance from the top of Steve's head to the hoop is also 12 feet.

Also the distance from the top of Steve's head and the top of Hoop is (10 - 5) feet = 5 feet.

Therefore calculating the distance from top of Steve's head to the hoop by using Pythagoras Theorem -

Let the required distance is d feet .

⇒  [tex]d = \sqrt{12^{2} + 5^{2} }[/tex]

⇒  [tex]d = \sqrt{169} = 13[/tex] feet

Therefore the distance from the top of Steve's head to the hoop is 13 feet.

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Answer:

  c. Reflect across the y-axis, translate 3 right and 2 down

Step-by-step explanation:

You want a description of the transformation of g(x) = ln(x) into f(x) = ln(3 -x) -2.

Reflection across the y-axis is the result of replacing x by -x in a function. That is, f(x) = g(-x) will reflect g(x) across the y-axis.

Translation right h units and up k units is the result of the transformation ...

  f(x) = g(x -h) +k

The given function f(x) can be written as ...

  f(x) = g(-(x -3)) -2

The first transformation is replacement of x by -x:

  f(x) = g(-x) . . . . . . . . reflection over the x-axis

The second transformation is replacement of x by x-3, and adding -2 to the function value:

  f(x) = g(-(x -3)) -2 . . . . translation of the reflected function right 3, down 2

The graph of g(x) = ln(x) is transformed to the graph of f(x) = ln(3 -x) -2 by reflection over the y axis, then translation right 3 and down 2, choice C.

315 > 131.5 > 131.05 > 13.15 > 1

Answer:

B is your answer

Step-by-step explanation:

Why this is, is because it is parallel an all four sides while a trapezoid isn't parallel on all four sides. So that means that B is not a trapezoid.

Figure B is not a trapezoid

A trapezoid is a quadrilateral with at least one pair of parallel sides.

The non-parallel sides may have different lengths, and its angles can vary.

It combines characteristics of both triangles and parallelograms in its geometric properties.

Figure A represents a trapezoid cos it has a lone pair of parallel lines.

Figure B is not a trapezoid but a parallelogram because it has 2 pairs of parallel lines.

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Answer:

The size of the small play area is [tex]400\ ft^{2}[/tex]

Step-by-step explanation:

Let

x-----> the small play area

y-----> the large play area

we know that

[tex]x+y=2,000[/tex] ----> equation A

[tex]x=\frac{1}{4}y[/tex]

[tex]y=4x[/tex] ----> equation B

substitute equation B in equation A and solve for x

[tex]x+(4x)=2,000[/tex]

[tex]5x=2,000[/tex]

[tex]x=2,000/5[/tex]

[tex]x=400\ ft^{2}[/tex]

Answer: B) Addition Property

Step-by-step explanation:

The Step 3 is: [tex]3x-30=0[/tex]

The idea is to solve the equation, which means that you have to find the value of the variable [tex]x[/tex].

As [tex]3x-30[/tex] is a subtraction, you need to add 30 to both sides of the equation to keep the equation balanced. This property is known as "Addition property of equality".

This property states that adding the same number to both sides of the equation, the equality does not change:

[tex]a=b\\a+n=b+n[/tex]

Then, the Addition property of equality applied in Step 3, get you to Step 4:

[tex]3x-30+(30)=0+(30)\\3x=30[/tex]

Answer: B. Addition Property

Step-by-step explanation:

Answer:

3 1/3

Step-by-step explanation:

The answer is 3 1/3 because 7 - 3 2/3 = 3 1/3

Answer:

3 1/3

Step-by-step explanation:

Answer:b

Step-by-step explanation:

Answer:

its the third one i got that

For this case we must simplify the following expression:

[tex]\frac {12y ^ 7} {18y ^ {- 3}}[/tex]

We have that by definition of properties of powers, it is fulfilled that:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Then, we can rewrite the expression:

[tex]12y ^ 7 * 18y ^ 3[/tex]

By definition of multiplication properties of powers of the same base we have:

[tex]a ^ m * a ^ n = a ^ {m + n}[/tex]

So:

[tex]12y ^ 7 * 18y ^ 3 = (12 * 18) * y ^ {7 + 3} = 216y ^ {10}[/tex]

Answer:

[tex]216y ^ {10}[/tex]

When y = 0 the expression is 0

Answer:

B

Step-by-step explanation:

Range of the graph is the ALLOWED y-values. The y-axis is number of gallons left in tank. So, it cannot be NEGATIVE number of gallons, so 0 is the lower limit of the range.

As we can see from the axis of the graph, we see where the line cuts the y-axis, that is the upper limit of number of gallons he starts off with. The y-intercept (y-axis cutting point) is 12.

So we can say that the range is  0 ≤ y ≤ 12

Correct answer is B

Answer:

1) The expression to represent the pattern is 11 + 8n

2) The expression to represent the pattern is 80 - 9n

Step-by-step explanation:

1) * Lets study the pattern;

- 19 , 27 , 35 , 43 , ..................

∵ 27 - 19 = 8

∵ 35 - 27 = 8

∵ 43 - 35 = 8

∴ The difference is constant between each two consecutive terms

∴ It is an arithmetic sequence

* Lets take about the arithmetic sequence

- If the first term is a and the constant difference is d

∴ a1 = a , a2 = a + d , a3 = a + 2d , a4 = a+ 3d , ........

∴ an = a + (n - 1)d, where n the position of the term in the sequence

* Now we will use this rule to find the expression of our pattern

∵ a = 19 , d = 8

∴ an = 19 + (n - 1)(8) ⇒ an = 19 + 8n - 8 ⇒ an = 11 + 8n

* Lets check it;

∵ a3 = 11 + 8(3) = 11 + 24 = 35 ⇒ true

∴ The expression to represent the pattern is 11 + 8n

2) * Lets study the pattern;

- 71 , 62 , 53 , 44 , ..................

∵ 62 - 71 = -9

∵ 53 - 62 = -9

∵ 44 - 53 = -9

∴ The difference is constant between each two consecutive terms

∴ It is an arithmetic sequence

* We will use the same rule above to find the expression of the pattern

∵ a = 71 , d = -9

∴ an = 71 + (n - 1)(-9) ⇒ an = 71 + -9n + 9 ⇒ an = 80 - 9n

* Lets check it;

∵ a4 = 80 - 9(4) = 80 - 36 = 44 ⇒ true

∴ The expression to represent the pattern is 80 - 9n

Answer:

[tex]946[/tex]

Step-by-step explanation:

we know that

The formula to find the sum is equal to

[tex]S=(a1+an)n/2[/tex]

where

a1 is the first term

an is the last term

n is the number of terms

In this problem we have

[tex]n=11[/tex]

[tex]a1=(98-2(1))=96[/tex]

[tex]an=(98-2(11))=76[/tex]

substitute the values in the formula

[tex]S=(96+76)(11/2)=946[/tex]

Set (x+3) to 0. X+3=0. X=-3

Set (x+2) to 0 X+2=0. X=-2

Answer:

B.  2004.

Step-by-step explanation:

f(x) =  100(1.0153)^x

When f(x) = 106 million:

106 = 100(1.0153)^x

(1 .0153)^x =   106/100 = 1.06

Taking logs:

x ln 1.0153 = ln 1.06

x = ln 1.06 / ln 1.0153

= 3.837

So  x = 4 years.

So the year is 2000 + 4 =  2004.

Answer:

2004

Step-by-step explanation: