Question 3 (5 points) Convert the decimal 0.929292... to a fraction.

The solution is x = √ 14, it is irrational

The closest integer approximation to the solution is 4

From the information given, we have that;

42 equals 3 x squared

This is represented as;

3x² = 42

Let's take the following steps to determine the value of x

Divide both sides by the coefficient of x²

x² = 42/3

x² = 14

Take the square root of both sides, we have;

x = √ 14

The solution is an irrational number

An irrational number is described as a number that cannot be expressed in a fractional form.

They are real numbers that expressed as quotients

Examples of irrational numbers are;

√5, √7, √11, √13

Now, let's find the square root, we have

= 3. 74

Take '7' as 1 and add to the whole number 3, we get;

= 4 ; to the closest integer

Hence, the value is 4

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Different possibilities for the given case are, 267540

4 railroads chosen from 15 class I railroads

2 railroads chosen from 8 class II railroads

1 railroad chosen from 7 class III railroads

So total combinations    = ¹⁵C₄ ˣ ⁸C₂ ˣ ⁷C₁

   = (15!)/(4!*11!) x (8!)/(2!6!) x (7!)/(1!6!)

   = 15 x 7 x 13 x 4 x 7 x 7 = 267540

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In the Mediterranean, the Mycenaeans rose to prominence by a mix of military prowess, economic connections, and cultural sway.

Thus, Military Might: The Mycenaeans had a strong military force and were expert warriors. They used sophisticated bronze weapons and chariot warfare as a tactic.

They were able to increase their influence and take control of neighbouring territories thanks to their military might.

Control over Trade Routes: The Mycenaeans had complete control over key trade routes in the Mediterranean, particularly those that extended from the Aegean to the eastern Mediterranean and beyond.

Thus, In the Mediterranean, the Mycenaeans rose to prominence by a mix of military prowess, economic connections, and cultural sway.

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a) The probability that exactly 2 of them have never been married is[tex]0.0026 \text{ or }2.6*10^{-3}[/tex]

b) The probability that at most 2 of them have never been married is[tex]0.0029\text{ or }2.9*10^{-3}[/tex]

c) The probability that at least 13 of them have been married is [tex]0.0046 \text{ or } 4.6*10^{-3}[/tex]

a)  What is the probability that exactly 2 of them have never been married?

By applying binomial probability distribution method,

[tex]P(x)=^{n}C_{x}p^{x}q^{n-x}[/tex]

Substitute,

P(x) =Binomial probability =  51% = 0.51

x = No. of times of an outcome = 2

n = No. of trials = 15

q =  Probability of failure = 49% = 0.49

[tex]^{n}C_{x}[/tex] = No. of combinations

[tex]P(2)=^{15}C_{2}*(0.51)^{2}*(0.49)^{15-2}\\\\P(2)=\frac{15!}{13!2!} *(0.51)^{2}*(0.49)^{13}\\\\P(2)=0.0026 \text{ or }2.6*10^{-3}[/tex]

b) What is the probability that at most 2 of them have never been married?

By applying binomial probability distribution method,

[tex]P(x)=^{n}C_{x}p^{x}q^{n-x}[/tex]

Substitute,

P(x) =Binomial probability =  51% = 0.51

x = No. of times of an outcome = 0,1,2

n = No. of trials = 15

q =  Probability of failure = 49% = 0.49

[tex]^{n}C_{x}[/tex] = No. of combinations

[tex]P(0-2)=^{15}C_{0}*(0.51)^{0}*(0.49)^{15-0}+^{15}C_{1}*(0.51)^{1}*(0.49)^{15-1}+^{15}C_{2}*(0.51)^{2}*(0.49)^{15-2}\\\\P(0-2) = 2.253*10^{-5}+15*0.51*4.59987*10^{-5}+2.563*10^{-3}\\\\P(0-2)=0.0029 \text{ or }2.9*10^{-3}[/tex]

c)What is the probability that at  least 13 of them have been married?

By applying binomial probability distribution method,

[tex]P(x)=^{n}C_{x}p^{x}q^{n-x}[/tex]

Substitute,

P(x) =Binomial probability =  51% = 0.51

x = No. of times of an outcome = 13,14,15

n = No. of trials = 15

q =  Probability of failure = 49% = 0.49

[tex]^{n}C_{x}[/tex] = No. of combinations

[tex]P(13-15)=^{15}C_{13}*(0.51)^{13}*(0.49)^{15-13}+^{15}C_{14}*(0.51)^{14}*(0.49)^{15-14}+^{15}C_{15}*(0.51)^{15}*(0.49)^{15-15}\\\\P(13-15)= 105*(0.51)^{13}*(0.49)^{2}+15* (0.51)^{14}*(0.49)+(0.51)^{15}\\\\P(13-15)= 0.0046 \text{ or } 4.6*10^{-3}[/tex]

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Answer: 01-2x > 3x - 6

Step-by-step explanation: distributive property

The third vertex of the isosceles triangle is (a/2, b).

Let one vertex of the triangle lies on the base of the x-axis as 'a' which is written as (a,0)

Similarly, the other vertex of the triangle lies on the base of the y-axis as 'b' which is written as (0,b)

Let other vertex be at origin (0, 0)

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

Hence, the vertex of the triangle is (a/2, b).

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Answer:

70

Step-by-step explanation:

f(1)=6, f(n)=f(n-1)+4

n = 1 → a1 = 6 ← given value

n = 2 → a2 = 6+4 = 10

n = 3 → a3 = 6+4+4 = 14

n = 4 → a4 = 6+4+4+4 = 18

n = 17 → a4 = 6+(4 * 16) =

(its 4 times 16 because 16 is 17 - 1 or n - 1)

n = 17 → a4 = 6+(64) = 70

socraticorg

Tony B

Answer:

24° , 60° , 96°

Step-by-step explanation:

sum the parts of the ratio, 2 + 8 + 5 = 15 parts

divide the sum of the angles in a triangle by 15 to find the value of one part of the ratio.

180° ÷ 15 = 12° , then

2 parts = 2 × 12° = 24°

5 parts = 5 × 12° = 60°

8 parts = 8 × 12° = 96°

the 3 angles in the triangle are 24° , 60° , 96°

Step-by-step explanation:

y varies INVERSELY as x.

that means

y = k/x

therefore,

22 = k/6

k = 22×6 = 132

and then, when y = 15

15 = 132/x

15x = 132

x = 132/15 = 8.8

consider

note that the letter g is common to all the numbers in the equation, so we take the lowest power of g and make a common factor, that is:

so the correct answer is

g(5g - 4)

Answer: 9g

Step-by-step explanation:

3g^2 + 2g^2 - 4g

you simplify the exponents first, because of P.E.M.D.A.S.:

9g + 4g - 4g combine like terms

Answer: 9g

Solution

Solution

The final answer

253.75 gallons remain in the tank when the depth of oil is 3.5 ft

Answer:

the length of AB is 9

Step-by-step explanation:

an isosceles triangle is a type of triangle i which two of its sides are equivalent(equal). let AB=AC=x

perimeter=22

                  perimeter=AB+AC+BC

                                22=x+x+4

                                 22-4=2x

                                      18/2=2x/2

                                           9=x

The amount of interest earned in 10 years is $75.

So, interest earned after 2 years = $15

Therefore, the amount of interest earned in 10 years is $75.

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Answer: The moon

Step-by-step explanation:

The cone is the solid form that represents "If you cut me in half, my end face will remain the same. Two of my faces are the same, one is curved."

The volume of a cone is defined as the amount of space occupied by a cone in a three-dimensional plane.

∵ The volume of the cone (V )= 1/3πhr²

The number of faces of a regular cone is one, which we may partition vertically into two halves.

This means one base face and lateral face

Now, the number of faces in one half equals the number of faces in the original form.

This meets the conditions outlined in the question.

So, the cone is a solid form.

Thus, the cone is the solid form that represents "If you cut me in half, my end face will remain the same. Two of my faces are the same, one is curved."

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The rates of changes of the given function for the corresponding intervals are:  [-5, -1] = -8, [-4, -1] = -7, [-3, -1] = -6, [-2, -1] = -5.

What is function?

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

This means that a function f will map an object x to exactly one object f(x) in the set of potential outputs if the object x is in the set of inputs (referred to as the domain) (called the codomain).

The rate of change of a function can be calculate using the formula:

[tex]R = \frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

Putting the value from the question:

given [x₁, x₂] = [-5, -1]

f(-5) = 35 , f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-35}{-1 -(-5)}[/tex]

R = -32/4

R = -8

given [x₁, x₂] = [-4, -1]

f(-4) = 24, f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-24}{-1 -(-4)}[/tex]

R = -21/3

R = -7

given [x₁, x₂] = [-3, -1]

f(-3) = 15, f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-15}{-1 -(-3)}[/tex]

R = -12/2

R = -6

given [x₁, x₂] = [-2, -1]

f(-2) = 8, f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-8}{-1 -(-2)}[/tex]

R = -5/1

R = -5

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The values x = 0, y = 0.03 and z = 0.039 for the three events A,B and C with their associated probabilities.

The following are axioms of probability for the purpose of answering the given question:

Two events are said to be mutually exclusive if the probability of their intersection is zero.

Two events are said to be independent if the probability of their intersection is equal to the product of their respective probability

From the question, the probability of the event A alone occurring=0.10

the probability of the event B alone occurring=0.30

the probability of the event C alone occurring=0.39

Given that B and C are mutually exclusive events;

x = probability of the intersection of B and C=0

A and C are said to be independent so; z = probability of the intersection of A and C = 0.10×0.39

probability of the intersection of A and C = 0.039

If A and B are not mutually exclusive events and are independent then;

y = probability of the intersection of A and B

probability of the intersection of A and B = 0.10×0.30

probability of the intersection of A and B = 0.03.

Hence, the values of x,y and z are 0, 0.03 and 0.039 respectively for the events A,B and C with their associated probabilities.

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The Solution:

Given the graph of f(x), we are required to determine whether the degree of the function is ODD or EVEN, and also to determine whether the function itself is ODD.

An odd function is defined as a function that has f(–x) = –f(x) for any value of x. The opposite input gives the opposite output.

From the given graph of f(x), the function f(x) is ODD.

The degree of the function f(x) is odd since the f(x) itself is odd.

It takes 1190 minutes for Allie to drive to the store and then to the car wash.

According to the question,

We have the following information:

Time taken by Allie to drive to the store = 456 minutes

Time taken by Allie to drive to the car wash from the store = 734 minutes

Now, we have to find the total time in minutes. So, we will add the total time taken by Allie to drive to the store and then to the car wash.

(Note that the time asked in the question is in minutes. So, we do not need to change the units of given time.)

Now,

The total time taken by Allie to drive to the store and then to the car wash = Time taken by Allie to drive to the store + Time taken by Allie to drive to the car wash from the store

The total time taken by Allie to drive to the store and then to the car wash = (456 + 734) minutes

The total time taken by Allie to drive to the store and then to the car wash = 1190 minutes

Hence, the total time taken by Allie to drive to the store and then to the car wash is 1190 minutes.

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-( ( 7 - u )( u - 2 ) ) is the factorized form of the polynomial -7u² + 12u + 4, using the AC method.

Given the polynomial in the question;

-7u² + 12u + 4

Factor out -1 out of the polynomial

-1( 7u² - 12u - 4 )

Compare to the form ax² + bx + c

To factor, compare to the form ax² + bx + c and rewrite the middle term as a sum of two terms whose product is;

a × c = 7 × -4 = -28

and whose sum is;

b = -12

Now, factor -12 out of -12x

-1( 7u² - 12(u) - 4 )

We know that -13 is the same as 2 plus -14

-1( 7u² - ( 2 - 14 )u - 4 )

Apply distributive property

-1( 7u² - 2u - 14u - 4 )

Group the terms

-1( u(7u - 2) - 2(7u - 2 ) )

-1( (7-u)(u-2) )

-( (7-u)(u-2) )

Therefore, the factorized form of the polynomial is -( ( 7 - u )( u - 2 ) ).

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-(7u+2)(u-2) is the factorized form of expression -7u²+12u+4.

An expression is combination of variables, numbers and operators.

The given expression is -7u²+12u+4.

We need to find the factors of this expression.

-7u²+12u+4.

This can be written as

-7u^2+14u-2u+4.

Take 7u from first two terms and 2 from last two terms in the expression.

-7u(u-2)-2(u-2)

(-7u-2)(u-2)

-(7u+2)(u-2)

Hence -(7u+2)(u-2) is the factorized form of -7u^2+12u+4.

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The equation of the line that is parallel to the line y = −2x +5 and passing through the point (1, −4) is y = -2x - 2.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

The slope of two parallel lines is always the same.

The slope y-intercept form of an equation is y = mx + c where m is the slope.

Given the parallel equation y = -2x + 5 by compare slope = -2

Therefore,the equation will become y = -2x + c

Substitute,(1,-4) into this

-4 = -2(1) + c ⇒ c = -2

So equation converts as y = -2x - 2.

Hence "The equation of the line that is parallel to the line y = −2x +5 and passing through the point (1, −4) is y = -2x - 2".

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The number that you can square to give an answer bigger than 500 but bigger than 600 = 25.

The square of a number is defined as the ability to multiple the given number by itself to give a perfect whole number.

For example the square of 2, which is written as 2² = 2×2 = 4

From the given scenario, the number that would be squared to give an answer bigger than 500 but bigger than 600 = 25

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Answer: the answer is B

So, as shown at the function

f(x) is constant at the middle interval (10 , 15)

at which f(x) = 2 and the digit 2 is constant

so, the answer is (10 , 15)

The slopes formed by each of the pairs of points are given as follows:

The slope is equivalent to the rate of change, hence, given two points, the slope is calculated as the change in y, also called rise, of these two points divided by the change in x, also called run.

For the first case, the points are:

(2, 11.9) and (4, 10.5)

Hence:

The slope is:

m = -1.4/2 = -0.7.

The other slopes are calculated as follows:

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Answer:  The slope is [tex]\frac{1}{2}[/tex].

Step-by-step explanation:

[tex]Slope = \frac{y_{2}-y_{1} }{x_{2}-x_{1} } =\frac{-1-2}{1-7} =\frac{-3}{-6} =\frac{3}{6}=\frac{1}{2}[/tex]

Answer:

40% of the number is 275.2.

Step-by-step explanation:

I am going to call the number x.

75% of the number: 0.75x

20% of the same number: 0.2x

The difference between 75% of a number and 20% of the same number is 378.4:

This means that:

0.75x - 0.2x = 378.4

0.55x = 378.4

x = 378.4/0.55

x = 688

40% of the number:

0.4*688 = 275.2

40% of the number is 275.2.

Probability of proportion will be greater than 3.18

Probability of Proportion: Probability represents the chances of some event happening. It is theoretical. Proportion summarizes how frequently some event actually happened

Population Proportion, p=0.52

sample proportion p'=0.45

sample size be n =436

probability of proportion will be greater than 52%

[tex]p(p' > 0.45)=p(p'-p\sqrt{p(1-p)/n} )[/tex]

[tex]=-p(z > (0.45-0.52)/\sqrt{0.52((1-0.52)/436}[/tex]

=P(z>-3.18)

probability of proportion will be greater than 3.18

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Paige's profit for the three-month period given the information provided in the question is $569.84.

Profit is the difference between total revenue and total cost. Revenue is the product of total units sold and the price per output.

Profit = revenue - cost

Revenue from selling the $15 bracelet = total bracelets sold for the 3 months x price of the bracelet

(8 + 11 + 22) x 15

41 x $15 = $615

Revenue from selling the $20 bracelet =  total bracelets sold for the 3 months x price of the bracelet

(7 + 6 + 14) x $20

27 x $20 = $540

Total revenue = $615 + $540 = $1,155

Total cost =  $292.58  x 2  = $585.16

Profit = $1,155 - $585.16 = $569.84

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Answer: x=59

Step-by-step explanation:

360-296=(x-24)+29

         64=x+5

         59=x

The length of the guy wire to the nearest foot is 42 feet.

The pole 5 ft tall is used to support the guy wire for the tower, which runs from the tower to a metal stake in the ground.

The situations forms a right angle triangle.

Therefore, the length of the guy wire can be found as follows:

Using trigonometric ratios, we can find the angle the guy wire made with the ground.

tan ∅ = opposite / adjacent

tan ∅ = 5 / 15

∅ = tan ⁻¹ 1 / 3

∅ = 18.4349488057

∅ = 18.43°

Therefore, let's find the length of the guy wire using the angle.

cos 18.43° =  adjacent / hypotenuse

0.94871060813 = 40 / h

h = 40 / 0.94871060813

h = 42.162488395

Therefore,

length of the guy wire = 42 feet

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