Determine if the following infinite series converges or diverges

The value of the expression is 0.0265. Using exponents and power rules, the required value is calculated.

The important exponent and power rules are:

The given expression is [tex]126^{-3/4}[/tex]

Using calculator: [tex]126^{-3/4}[/tex] = 0.0265

Applying the exponent rule for evaluating the given expression:

[tex]126^{-3/4}[/tex]

Applying the negative power rule;

I.e., a⁻ⁿ = 1/aⁿ

⇒ [tex]126^{-3/4}=\frac{1}{126^{3/4}}[/tex]

Applying fractional exponent rule;

I.e., [tex]a^{\frac{x}{y} } = \sqrt[y]{a^x}[/tex]

⇒ [tex]\frac{1}{126^{3/4}}=\frac{1}{\sqrt[4]{126^3} }[/tex]

⇒ 1/[tex]\sqrt[4]{2000376}[/tex]

⇒ 1/37.6077

⇒ 0.0265

Therefore, the value of the given expression is 0.0265.

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Answer:

[tex]3.24*10^8[/tex]

Step-by-step explanation:

First, it is even so you don't need a negative power. Secondly, you put the decimal point after the first number which is three, and the next numbers which are not zeros go after it. Then you count the two numbers behind the decimal and the rest of the zeros. Then the number you get is the power of 10. And then just multiply and check your answer. :)

TRUE

The safety triangle tries to predict safety performance.

The accident triangle, also known as Heinrich's triangle or bird's triangle, is a theory of occupational injury prevention. Indicates the relationship between serious accidents, minor accidents, and near misses. The idea is that the fewer minor accidents, the fewer serious accidents.

The process safety triangle is used to illustrate the different actions that can lead to an accident. This tool has a bottom up flow where each layer can be thought of as a preventative measure to the layer above it.

One of the main purposes of the process safety triangle is to explain how unsafe actions can lead to serious accidents. The Process Safety Triangle is also used to visualize different layers of protection and redesign systems to ensure better preventive practices. The lowest level of unsafe actions is categorized as the primary metric. A leading indicator is a preventive action taken to prevent an incident from occurring. Dangerous behavior by employees. B. Not wearing personal protective equipment or missing a system layer of protection is a major cause of process safety incidents. The wider the base of the process safety triangle, the wider the top level. This triangle shows that the more unsafe your actions are, the more likely you are to die in a process safety incident.

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The probability of the frequency of an event in repeated trials under comparable circumstances is a statistical analysis.

The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to an issue in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.

Finding the distribution hidden in your data is the aim of a statistical analysis. What do you mean by the distribution that lies underlying my data? "The distribution of your data describes the peaks and valleys of its characteristics in relation to a target population.

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[tex]\mathbf{u} =\langle -6, -10 \rangle \\ \\ \mathbf{v}=\langle 7,8 \rangle \\ \\ \mathbf{u} \cdot \mathbf{v}=(-6)(7)+(-10)(8)=-122 \\ \\ \therefore -3(\mathbf{u} \cdot \mathbf{v})=-3(-122)=\boxed{366}[/tex]

The value of -3(u•v) is 366 when vector u= -6i - 10j and vector v=-6i - 10j is given.

The dot product of two vectors is the sum of the products of their corresponding components.

Here, u= -6i - 10j, from the figure as u goes 6 coordinate left to the y axis and and 10 coordinates below the x axis.

v= 7i + 8j, from the figure as v corrdinates right to the y axis and 8 coordinats upwards to the x axis.

Therefore u.v= (-6i - 10j).(7i + 8j)

                      = -42 - 80

                      = -122

So, -3(u.v)= (-3)×(-122)

                =366

Hence, the value of -3(u•v) is 366

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From the given options, the rational numbers is:

17.156 = 17,156/100

Which is the one in option C.

A rational number is a number that can be written as the quotient of two integer numbers.

When written in decimal form, a rational number has a finite number of digits after the decimal point. Now, for the given options we have:

A: √15

B: 2.6457513110...

C: 17.156

D: √3/85

Now, the square root of a number that is no square, is always an irrational number, so we can discard these two, and also we can see that the number in option B has infinite digits after the decimal point, so we also discard that one.

Now, if we look at the remaining option, which is:

17.156

We can multiply it and divide it by 100 to get:

(100/100)*17.156 = 17156/100

So the number can be written as the quotient of two integers, which means that it is a rational number.

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The completed equations are:

2x + 3y = 80 equation 1

x + y = 37 equation 2

In order to determine the number of each type of shots made, two equations would be derived based on the information provided in the question. These equations would be solved simultaneously in order to determine the required values.

[(type of basket made)x ]+ [(type of baskets made)y] = total number of points

2x + 3y = 80

x + y = total number of baskets

x + y = 37

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This relates to combination and permutations and the number of distinct arrangements that are possible will be 6.

From the information, a mathematical prodigy wishes to put 2 of his indistinguishable IMO gold medals and 2 of his indistinguishable IPhO gold medals in one row.

Let 1 = IMO

Let 0 = IPho.

Therefore, the number of arrangement will be:

0011

0110

1100

1010

0101

1001

Therefore, the number of arrangement will be 6.

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Using a linear function, the correct option regarding the situation is given by:

C) 57 ≤ 1.28x + 38 ≤ 87; To stay within the range, the usage should be between 14.8 and 38.3 HCF.

A linear function is modeled by:

y = mx + b

In which:

The bill is modeled by a linear function, with an intercept of $38 and a slope of $1.28, hence it is given by:

C(x) = 1.28x + 38

The bill should be between $57 and $87 dollars per month, hence:

57 <= C(x) <= 87.

The values of x are:

C(x) >= 57

1.28x + 38 >= 57

x >= 19/1.28

x >= 14.8.

C(x) >= 87

1.28x + 38 >= 87

x >= 49/1.28

x >= 38.3.

Hence option C is correct.

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The length of each of the equal sides is become x = (3y-4) cm

According to the statement

we have given that the perimeter of the isosceles triangle and length of third side. and we have to find the length of same side of triangle.

So,

An isosceles triangle is a triangle that has two sides of equal length.

Let the equal sides of isosceles triangle be x cm each.

We know that the

Sum of sides of a triangle = perimeter

x+x+(3y-7) = 9y-15

2x = 9y-3y-15+7

After solving the equation it become

2x= 6y-8

x=(6y-8)/2

Now the length of equal sides is x=3y-4

So, The length of each of the equal sides is become x = (3y-4) cm

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The conclusion that can be made from the data is that the probability illustrates that the employees who regularly leave for work late as less likely to receive a speeding ticket than employees who regularly leave for work early or on time.

It should be noted that probability simply means the likelihood of the occurence of an event.

In this case, the survey was given to randomly selected employees who drive to work and eagh employee was asked to report if they had received a speeding ticket on their morning commute to work any time in the last year.

Therefore, the conclusion is that the the employees who regularly leave for work late as less likely to receive a speeding ticket than employees who regularly leave for work early or on time.

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Answer: B: The probability of an employee receiving a speeding ticket given that they regularly leave for work early or on time is less than the probability of an employee not receiving a speeding ticket given that they regularly leave for work late.

Step-by-step explanation:

trust me :)

Answer:

x = 36

Step-by-step explanation:

The two lines are parallel and intersected by a transversal line.

The co-interior angles formed will sum up to 180°

Here angles 3x and 2x are the co-interior angles

So 3x + 2x = 180

5x = 180

x = 180/5 = 36

Answer:

Step-by-step explanation:

2x + 2x + 3x + 3x = 180°

10x = 180°

x = 180° : 10 =

x = 18°

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

check

2 × 18 + 2 × 18 + 3 × 18 + 3 × 18 = 180°

the answer is good

Measurement refers to a process through which the dimensions, size (weight), or other physical quantities of magnitude that are associated with an object or land is taken, especially for use in a scientific research and experiment such as direct comparison.

From the odometer on Missy's car, we have the following information:

Initial reading = 23,678 miles.

Final reading = 25,127 miles.

Trip = Final reading - Initial reading

Trip = 25,127 - 23,678

Trip = 1,449 miles.

Lubrication mileage = 16,000 kilometers.

Total mileage = 68,000 kilometers.

Lubrication time = Total mileage/Lubrication mileage

Lubrication time = 68,000/16,000

Lubrication time = 4.25 ≈ 4.

Next Lubrication time = (16,000 × 0.25) + 68,000

Next Lubrication time = 16,000 - (16,000 × 0.25) + 68,000

Next Lubrication time = 80,000 kilometers.

Rate = $29 per mile

Speed limit = 35 mph

Missy's car speed = 43 mph

Difference = 43 - 35

Difference = 8 mph.

Ticket = 29 × 8

Ticket = $232.

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Answer:

y = 3

Step-by-step explanation:

(5y - 3)/4 + 6 = 3y

5y - 3 + 24 = 12y

7y = 21

y = 3

Check.

(5*3 - 3)/4 + 6 = 3*3

(15 - 3)/4 + 6 = 9

12/4 + 6 = 9

3 + 6 = 9

9 = 9

Answer: y = 3

Step-by-step explanation:

Given equation

[tex]\frac{5y~-~3}{4} ~+~6~=~3y[/tex]

Multiply 4 on both sides (to eliminate fraction)

[tex]\frac{5y~-~3}{4} *4~+~6*4~=~3y*4[/tex]

[tex](5y~-~3)~+~24~=~12y[/tex]

Expand parenthesis and combine like terms

[tex]5y~-~3~+~24~=~12y[/tex]

[tex]5y~+~21~=~12y[/tex]

Subtract 5y on both sides

[tex]5y~+~21~-~5y~=~12y~-~5y[/tex]

[tex]21~=~7y[/tex]

Divide 7 on both sides

[tex]21~/~7~=~7y~/~7[/tex]

[tex]\Large\boxed{y=3}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The value of c, the constant of the function y = ax² + bx + c, exists -3.

An equation exists as an expression that indicates the relationship between two or more numbers and variables.

Given that: y = ax² + bx + c

At point (4, 21)

21 = a(4²) + 4b + c .......(1)

At point (5, 32)

32 = a(5²) + 5b + c .........(2)

At points (6, 45)

45 = a(6²) + 6b + c .......(3)

Therefore, the value of a = 1, b = 2 and c = -3.

The value of c, the constant of the function y = ax² + bx + c, exists -3.

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[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&96\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&160\\ \qquad \textit{of the object}\\ h=\textit{object's height}&h\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+96t+160[/tex]

Check the picture below.

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+96}x\stackrel{\stackrel{c}{\downarrow }}{+160} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 96}{2(-16)}~~~~ ,~~~~ 160-\cfrac{ (96)^2}{4(-16)}\right) \implies \left( - \cfrac{ 96 }{ -32 }~~,~~160 - \cfrac{ 9216 }{ -64 } \right)[/tex]

[tex](3~~,~~160 + 144)\implies \underset{~\hfill feet}{\stackrel{seconds~\hfill }{(\stackrel{\downarrow }{3}~~,~~\underset{\uparrow }{304})}}[/tex]

The paragraph looks like:

Since AC, MN, and DB intersect at O, ∠AOM ≅ ∠NOC and ∠MOD ≅ ∠BON by the vertical angles theorem. It is given that ∠BON ≅ ∠NOC, so by the transitive property of congruence, ∠AOM ≅ ∠MOD.

In the question, we are asked to convert the given proof to the paragraph format, where the proof is already given to us.

The proof given to us is:

Statements________________________Reasons

1. AC, MN, and  DB intersect at O.______1. given

2. ∠AOM ≅ ∠NOC__________________2. vertical angles theorem.

3. ∠MOD ≅ ∠BON__________________3. vertical angles theorem.

4. ∠BON ≅ ∠NOC__________________4. given.

5. ∠AOM ≅ ∠MOD_________________5. transitive property of congruence.

To convert this proof to the paragraph format, we need to translate each statement along with its reason in the paragraph.

Thus, the paragraph looks like:

Since AC, MN, and DB intersect at O, ∠AOM ≅ ∠NOC and ∠MOD ≅ ∠BON by the vertical angles theorem. It is given that ∠BON ≅ ∠NOC, so by the transitive property of congruence, ∠AOM ≅ ∠MOD.

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Answer:

Infinite

Step-by-step explanation:

12x 8 = 12x 8

Infinitely many solutions, as left side = right side.

Answer:

7.a) 5

7.b) 1/2

8. 1

Step-by-step explanation:

7.

a)

Read the points on the graph (0, 0) and (1, 5).

slope = (5 - 0)/(1 - 0) = 5/1 = 5

b)

read the points on the graph (0, 0) and (4, 2).

slope = (2 - 0)/(4 - 0) = 2/4 = 1/2

8.

Points (1, 4) and (5, 8)

slope = (8 - 4)/(5 - 1) = 4/4 = 1

The multiplication property of equality has been used in the second step when both sides of the equation have been multiplied by 5/3.

State the Multiplication Property of Equality:

The Multiplication Property of Equality states that multiplying both sides of the equation with the same number, expression, or variable, the equation remains unchanged, i.e. equality is maintained.

Use of Multiplication Property of Equality in the Second Step:

The given equation was,

3x/5 + 5 = 20

In the first step, subtraction property of equality is applied as follows,

3x/5 + 5 - 5 = 20 - 5

3x/5 = 15

Now, for isolating x on the left hand side, we must apply multiplication property of equality by multiplying both sides of the equation by 5/3.

We get,

3x/5 × 5/3 = 15 × 5/3

x = 25

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The angle m∠A can be represented as follows:

The above circle, a secant and a tangent intersect outside the circle.

A secant is a straight line that intersects a circle in two points.

A tangent  is a line that never enters the circle's interior.

Therefore, when a secant and a tangent intersect, the following rules applies:

m∠A = 1 / 2 (BD - BC)

m∠A = 1 / 2 (164 - 70)

m∠A = 1 / 2 (94)

m∠A = 47 degrees.

Therefore, the angle m∠A can be represented as follows:

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The equation 2^x = 128 as a logarithmic equation is log₂(128) = x

The equation is given as:

2^x = 128

Take the logarithm of both sides

log(2^x) = log(128)

Rewrite as:

x * log(2) = log(128)

Divide both sides of the equation by log(2)

x = log(128)/log(2)

Apply the change of base rule

x = log₂(128)

Hence, the equation 2^x = 128 as a logarithmic equation is log₂(128) = x

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Answer:

If  m(x) = x^3 - x^2 - 5x - 3 then x - 3 is a factor.

Step-by-step explanation:

By the Factor Theorem if  (x - a) is a factor of f(x) then f(a) = 0.

m(x) = x^3 - x^2 - 5x - 3

m(3) = 27 -  9  - 15 - 3 = 0

- so x - 3 is a factor

Answer:

  √3 is irrational

Step-by-step explanation:

The location of the third point of a triangle can be found using a rotation matrix to transform the coordinates of the given points.

With reference to the attached figure, the slope of line AC is √3, an irrational number. This means the line AC never passes through a point with integer coordinates. (Any point with integer coordinates would be on a line with rational slope.)

The line segments making up an equilateral triangle are separated by an angle of 60°. If two vertices are on grid squares, the third must be a rotation of one of them about the other through an angle of 60°. The rotation matrix is irrational, so the rotated point must have irrational coordinates.

The math of it is this. For rotation of (x, y) counterclockwise 60° about the origin, the transformation matrix is ...

  [tex]\left[\begin{array}{cc}\cos(60^\circ)&\sin(60^\circ)\\-\sin(60^\circ)&\cos(60^\circ)\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}x'\\y'\end{array}\right][/tex]

Cos(60°) is rational, but sin(60°) is not. For any non-zero rational values of x and y, the sum ...

  cos(60°)·x + sin(60°)·y

will be irrational.

As in the attached diagram, if one of the coordinates of the rotated point (B) is zero, then one of the coordinates of its image (C) will be rational. The other image point coordinate cannot be rational.

The value of length HL is 8.

A secant is a line that intersects a circle in exactly two points

When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other.

Therefore,

(EF + FL)FL = HL(GH + HL)

(10 + 14)10 = (HL + 30 - HL)HL

240 = 30(HL)

divide both sides by 30

Hence,

240 / 30 = 30HL / 30

8 = HL

Therefore,

HL = 8

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Answer:

a. triangle DEF's lines are all 3 times more than triangle ABC

b. triangle DEF's lines are all 3 times more than triangle ABC

c. 2.5 times 2 = 5

I hope u can elaborate a bit more :)

Answer:

$149.25

Step-by-step explanation:

The discount is 15% of $995

[tex]15\%\times995[/tex]

Note that percentages can also be written as that number over 100.

[tex]\frac{15}{100}\times995[/tex]

Simplify the fraction

[tex]\frac{3}{20}\times995=\frac{2985}{20}=149.25[/tex]

Therefore the discount is $149.25.

Answer:

$149.25

Step-by-step explanation:

Multiply = add powers

3 + - 1 = 2

- - means +

+ + means +

- + means -

Thus, answer is 2^2

Hope this helps!