Horizontally translated 4 units left, vertically translated 2units down, and shrunk vertically by one half.

The probability P(5 ≤ x ≤ 9) is 0.6847

Assume that x has a normal distribution

We have been the mean and standard deviation μ = 6; σ = 2.

To calculate this probability we use the standardized normal distribution and the z-value for 5 and 9.

z = (5 - 6)/2

  = -0.5

and z = (9 - 6)/2

         = 1.5

Then the probability is calculated as:

P(x ≤ 5) = 0.3085

P(x ≤ 9) = 0.9932

P(5 ≤ x ≤ 9) = 0.9932 - 0.3085

P(5 ≤ x ≤ 9) = 0.6847

Therefore, the probability P(5 ≤ x ≤ 9) is 0.6847

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Answer:

0≤x≤|R

Step-by-step explanation:

I'm not really sure but I think the domain is all positive real numbers including zero

Answer:

x=38

Step-by-step explanation:

The are supplementary. This is because the 2 lines are parallel and the corresponding angle to 2x-15 is supplementary. And because corresponding angles are congruent 2x-15 and 3x+5 are supplementary.

2x-15+3x+5=180

5x-10=180

5x=190

x=38

We know that

• The height is 5 meters.

• The cable is 7 meters long.

Using the given information, we can represent the situation with a diagram.

In the diagram above you can observe that the x is a leg of the right triangle. So, we have to use Pythagorean's Theorem to find x.

Then, we solve for x.

Answer: The answer is 15

Step-by-step explanation: 25*  3/5 is 15 so 15 out of 25 is what percent of the class has brown eyes

To write a number in scientific notation you must know:

1. A number in scientific notation is written as the product of a number (integer or decimal) and a power of 10

2. A number can be converted to scientific notation by increasing the power of 10 by one for each place the decimal point is shifted to the left.

Then so:

Answer:

Yes

Step-by-step explanation:

This is the correct answer good job!

the tuition at a certain college was $29,694 last year

Intial Tution fees of college = $29,694

increased 5.6% from last year to the current year

i.e. Increased fees amonut = 5.6% of intial fees

So, tution of college at present year is : Intial Tution fees of college+ 5.6% of intial fees

So, This year tution fees is $31356.864

In the nearest dollars it will be: $31357

Answer:

1. b = 2A/h

2. h = 2A/b

Step-by-step explanation:

All you have to do is isolate the variable.

1.

Isolate b:

A = 1/2 x b x h

Multiply each side by 2

2A = b x h

Isolate b by dividing both sides by h

b = 2A/h

2.

Isolate h:

A = 1/2 x b x h

Multiply each side by 2

2A = b x h

Isolate h by dividing both sides by b

h = 2A/b

Answer:

Almost!

Step-by-step explanation:

Problems 1-9 and 11 are correct, but not problem 10 or 12

For problem 10, 12/6 does equal 6/1, so it would just be the whole number of 6 as your final answer as it doesn't need to be simplified further.

For problem 12, -4/6 can be simplified further to -2/3 by dividing by 2.

Answer: Very close!

Step-by-step explanation:

Problems 7, 8, 9, and 11 are correct but not 10 or 11, because they are not in simplest form.

2/1 can be simplified to 2, and -4/6 can be simplified to -2/3.

Answer:

Step-by-step explanation:

Neither, they are not congruent.

Let x represents the number of months it will take Kelsey to have more money than Kyle.

Given that Kelsey starts with $150 in her account and she adds $25 a month, it means that the amount that he would have saved after x months is

150 + 25 *x

= 150 + 25x

Given that Kyle starts with $200 in his account and adds $20 a month to his account, it means that the amount that he would have saved after x months is

200 + 20 *x

= 200 + 20x

For Kelsey to have more money than Kyle, the inequality would be

150 + 25x > 200 + 20x

25x - 20x > 200 - 150

5x > 50

it is 2 becuase 1 plus 1 is two when you have an apple and a freind gives you an apple you have 2 appelapples

Answer:

1+1=2

Step-by-step explanation:

if you have one of me then you duplicate me or make a dopleganger than you now have 2

have a great day^^

a) Total purchase price for the bicycle is $19,145

b) The difference between the hire purchase price and the cost price for the bicycle is $2,825.50

c) The percentage of difference between the hire purchase price and the cost price for the bicycle is 17%

Percentage:

Percentage means a fraction or a ratio in which the value of whole is always 100.

Given,

A bicycle has cash price $16,319.50. It can be bought on hire purchase with a deposit of $6,900 and ten monthly installments of $1,224.50 each.

Here we need to following:

a) Purchase price for the bicycle

b) Difference between the hire purchase price and the cost price for the bicycle

c) Percentage of the cash price.

The total purchase price is calculated by adding the deposit and the ten month installment.

So, the total purchase price is,

=> 6900 + (10 x 1224.50)

=> 6900 + 12245

=> 19145.

Therefore, the total purchase price is $19145.

Now, the difference between the hire purchase price and the cost price for the bicycle is calculated as,

=> 19145 - 16319.50

=> 2825.50

So, the difference between the hire purchase price and the cost price for the bicycle is $2,825.50

Now, we have to calculate the percentage by using the following expression,

x% of 16,319.50 = 2825.50

x% = 2825.50/16319.50

x% = 0.1731

x = 17.31.

Therefore, there is 17% difference in the hire purchase price and the cost price for the bicycle.

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The product of 4 1/10 and -3 5/12 is -14 1/120

Fractions are simply described as a subset of a whole or the part of a whole.

They are several types of fractions, some of which includes;

Some examples of mixed fractions; 3 1/4, 5 1/2, 6 1/4

Some examples of simple fractions; 1/2, 1/4, 1/6

Some examples of proper fractions; 3/4, 4/5, 6/7

Some examples of improper fractions; 3/2, 4/3, 6/5

Given the mixed fractions;

4 1/10  ×  -3 5/12

convert to improper fractions

41/10 × - 41/12

Multiply through

- 1681/120

Find the ratio

- 14 1/ 120

Hence, the value is - 14 1/ 120

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Yahtzee is a game of chance like dice or poker. The numbers of ways the outcomes ( straight rolling ) is 240 .

Probability of hitting a large straight is 240 / 7776 = 1/32

Yahtzee is the one of dice game that uses five standard six-sided dice. After rolling each die, the player can decide which die to keep and which to reroll. Goals include many different types of combinations, many of which originate from poker.

The two types of combinations that players must roll are called roads: small roads and large roads. Similar to poker straights, these combinations consist of consecutive dice. A small straight uses 4 out of the 5 dice and a large straight uses all 5 dice. Since the dice rolls are random, we can use probability to analyze the likelihood of hitting large straight on a single roll. Assumes that the dice used are fair and independent of each other. Now, you need to know how many ways you can roll a big/ large straight. Here it is more difficult than calculating the sample size. Big straights are harder to roll than small straights, but it’s easier to count the number of times you’ve rolled a big straight than the number of times you’ve rolled a small straight.

Next, determine the number of ways to get a straight by rolling the given dice. To get a nice straight with dice {1, 2, 3, 4, 5}, you can arrange the dice in any order. It turns out that you just swap the five dice. There are 5! = 120 ways to do this. There are two dice combinations that form the large Straight, each with 120 ways to roll, so there are 2 x 120 = 240 ways to roll the large Straight.

Now the probability of hitting a big/ large straight can be calculated with simple division. Since there are 240 ways to get the big straight in one roll, and 7776 rolls 5 dice, the odds of getting the big straight are 240/7776, close to 1/32, and lie 3.1%.

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The zero of the function is 25.6 and it means that the total number of days is 25.6

From the question, the equation of the function is given as

c = 6.4 - 0.25p

The zero of this function is when the function equals 0

This is represented as

c = 0

Substitute c = 0 in c = 6.4 - 0.25p

So, we have

6.4 - 0.25p = 0

The above equation becomes

0.25p = 6.4

Divide both sides by 0.25

p = 25.6

So, the zero is 25.6 and it represents that the total number of days

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Kayleigh have 25 nickels with her.

Given,

The total value of coins Kayleigh have = $5.50

Number of quarters with Kayleigh = 17 quarters

We have to find the number of nickels Kayleigh with her.

Lets see:

1 dollar = 4 quarters

1 dollar = 20 nickels

Here, we have a total of 5.50 dollar

In this, 17 quarters are there.

So,

17 / 4 = 4.25

That is, the value of coins as quarters is $4.25

Now,

5.50 - 4.25 = 1.25

That is,

$1.25 is in the form of nickels.

Number of nickels = 1.25 × 20

Number of nickels = 25

Therefore,

Kayleigh have 25 nickels with her.

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If ABC is a triangle, which when plotted on the cartesian coordinate system, has it's vertices at A(4, 1), B(-3, -2), and C(-1, 3), then the perimeter of triangle ABC will be [√58/(√2 - 1)]

As per the question statement, ABC is a triangle, which when plotted on the cartesian coordinate system, has it's vertices at A(4, 1), B(-3, -2), and C(-1, 3).

We are required to calculate the perimeter of triangle ABC.

To solve this question, first we need to calculate the distances between AB, BC ad AC, which are the three sides of our concerned triangle ABC, and then add them up to obtain our desired answer. And to calculate the lengths of AB, BC ad AC, we will need to use the distance formula which goes as,

"The distance between any two points (x₁, y₁) and (x₂, y₂) can be given by

√[(x₂ - x₁)² + (y₂ - y₁)²]

Considering points A(4, 1) and B(-3, -2), we can say that [(x₁, y₁) = (4, 1)] and [(x₂, y₂) = (-3, -2)]. Therefore, distance AB = √[{(-3) - 4}² + {(-2) - 1}²]

Or, AB = √[{-(3 + 4)}² + {-(2 + 1)}²]

Or, AB = √[(-7)² + (-3)²]

Or, AB = √[(49 + 9)]

Or, AB = √58

Similarly considering points A(4, 1) and C(-1, 3), we can say that

[(x₁, y₁) = (4, 1)] and [(x₂, y₂) = (-1, 3)].

Therefore, distance AB = √[{(-1) - 4}² + (3 - 1)²]

Or, AC = √[{-(1 + 4)}² + (3 - 1)}²]

Or, AC = √[(-5)² + (2)²]

Or, AC = √[(25 + 4)]

Or, AC = √29

Finally considering points B(-3, -2) and C(-1, 3), we can say that

[(x₁, y₁) = (-3, -2)] and [(x₂, y₂) = (-1, 3)].

Therefore, distance BC = √[{(-1) - (-3)}² + {3 - (-2)}²]

Or, BC = √[{-(1) + 3}² + (3 + 2)²]

Or, BC = √[(3 - 1)² + (5)²]

Or, BC = √[(4 + 25)]

Or, BC = √29

Therefore, the perimeter of Triangle ABC  = (AB + BC + AC)

Or, perimeter of Triangle ABC  = (√58 + √29 + √29)

Or, perimeter of Triangle ABC  = [√(29 * 2) + √29 + √29]

Or, perimeter of Triangle ABC  = [(√29*√2) + √29 + √29]

Or, perimeter of Triangle ABC  = √29(√2 + 1 + 1)

Or, perimeter of Triangle ABC  = √29(√2 + 2)

Or, perimeter of Triangle ABC  = (√29*√2)(1 + √2)

Or, perimeter of Triangle ABC  = (√58)(1 + √2)

Or, perimeter of Triangle ABC  = [tex]\frac{\sqrt{58} (1+\sqrt{2})(1-\sqrt{2}) }{(1-\sqrt{2})} =\frac{\sqrt{58} [(1)^{2}-(\sqrt{2})^2 }{(1-\sqrt{2})}}[/tex]

Or, perimeter of Triangle ABC  = [tex]\frac{\sqrt{58} [(1-2) }{(1-\sqrt{2})}}=\frac{-\sqrt{58}}{(1-\sqrt{2})}}=\frac{\sqrt{58}}{(\sqrt{2}-1)}}[/tex]

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a)The percentage of bottles expected to have a volume more than 32 oz is 33.60%

b) 85% of 0.3360 is 0.2856

a) The volumes of soda in quart soda bottles can be represented by a Nomal model with a= 32.3 oz

b=8.8 oz

Let S be the volume of randomly selected soda bottles

Y-score: S-a/b

For S=32 oz

Substitute the values of S,a and b into the equation

Y=32-32.3/8.8

Y= - 0.0341

Probability of bottles that have a volume more than 32 oz is

P(S>32)=P(Y>-0.0341)= 0.3360

Percentage of bottles that have volume more than 32 oz will be

0.3360×100%=33.60%

b) 85% of 0.3360 is 0.2856

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Answers:

[tex](f+g)(\text{x}) = \boldsymbol{2\text{x}^2+2\text{x}-12}[/tex]

Domain = set of all real numbers

========================================================

Work Shown:

[tex](f+g)(\text{x}) = f(\text{x})+g(\text{x})\\\\(f+g)(\text{x}) = (2\text{x}^2+\text{x}-11)+(\text{x}-1)\\\\(f+g)(\text{x}) = 2\text{x}^2+\text{x}-11+\text{x}-1\\\\(f+g)(\text{x}) = 2\text{x}^2+(\text{x}+\text{x})+(-11-1)\\\\(f+g)(\text{x}) = 2\text{x}^2+2\text{x}-12\\\\[/tex]

The domain of each f(x) and g(x) is "set of all real numbers" since we can replace x with any real number to get some output.

By extension, this means the domain of (f+g)(x) is also "set of all real numbers".

It turns out any polynomial will have this domain. We don't have to worry about things like applying square roots to negatives, or dividing by zero. This is why there isn't a restriction on x.

To write "set of all real numbers" in interval notation, we would say [tex](-\infty, \infty)[/tex] to indicate x is anything between negative infinity and positive infinity.

Answer:

see explanation

Step-by-step explanation:

there are 15 students , 9 of which are boys, then

number of girls = 15 - 9 = 6

ratio of boys : girls = 9 : 6 = 3 : 2 ← in simplest form

All the dimensions of the shape is found as 19 ft.

For the given question, the dimensions of the shape is given as;

The perimeter of the shape = 76 ft.

The formula of the perimeter = sum of length of all sides.

Let 'P' be the perimeter.

P = (4x-5) + (25-x) + (13 + x)  + (3x+1) ing

Simplifying

P = 4x - x + x + 3x - 5 + 25 + 13 + 1

76 = 7x + 34

7x = 76 - 34

7x = 42

x = 6

Thus, the dimensions of the shape is; Put x = 6

Thus, all the dimensions of the shape is found as 19 ft.

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Solution given to both questions below, they reveal the given answers.

The steps are self-explanatory, let me know if anything is unclear.

Answer:

[tex]\textsf{24.} \quad \dfrac{1}{(x-2)(x-3)}[/tex]

[tex]\textsf{25.} \quad x=1, \quad x=-1[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{2}{(x-2)(x-3)}+\dfrac{2}{(x-1)(3-x)}+\dfrac{1}{(1-x)(2-x)}[/tex]

When adding rationals with different denominators, make the denominators the same by finding the least common denominator.

Create a common denominator by:

[tex]\textsf{Multiplying the first fraction by $\dfrac{x-1}{x-1}$}.[/tex]

[tex]\textsf{Multiplying the second fraction by $\dfrac{-(x-2)}{-(x-2)}$}.[/tex]

[tex]\textsf{Multiplying the third fraction by $\dfrac{x-3}{x-3}$}.[/tex]

[tex]\implies \dfrac{2}{(x-2)(x-3)} \cdot \dfrac{x-1}{x-1}+\dfrac{2}{(x-1)(3-x)}\cdot \dfrac{-(x-2)}{-(x-2)}+\dfrac{1}{(1-x)(2-x)}\cdot \dfrac{x-3}{x-3}[/tex]

[tex]\implies \dfrac{2(x-1)}{(x-1)(x-2)(x-3)}+\dfrac{-2(x-2)}{-(x-1)(x-2)(3-x)}+\dfrac{x-3}{(1-x)(2-x)(x-3)}[/tex]

[tex]\implies \dfrac{2(x-1)}{(x-1)(x-2)(x-3)}+\dfrac{-2(x-2)}{(x-1)(x-2)(-3-(-x))}+\dfrac{x-3}{(-(-1+x))(-(-2+x))(x-3)}[/tex]

[tex]\implies \dfrac{2(x-1)}{(x-1)(x-2)(x-3)}+\dfrac{-2(x-2)}{(x-1)(x-2)(x-3)}+\dfrac{x-3}{(x-1)(x-2)(x-3)}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{d}+\dfrac{b}{d}+\dfrac{c}{d}=\dfrac{a+b+c}{d}:[/tex]

[tex]\implies \dfrac{2(x-1)-2(x-2)+(x-3)}{(x-1)(x-2)(x-3)}[/tex]

Expand the numerator:

[tex]\implies \dfrac{2x-2-2x+4+x-3}{(x-1)(x-2)(x-3)}[/tex]

[tex]\implies \dfrac{x-1}{(x-1)(x-2)(x-3)}[/tex]

Cancel the common factor (x - 1):

[tex]\implies \dfrac{1}{(x-2)(x-3)}[/tex]

Given equation:

[tex](4x-1)(x+2)=2+7x[/tex]

Expand the left side:

[tex]\implies 4x^2+7x-2=2+7x[/tex]

Subtract 7x from both sides:

[tex]\implies 4x^2+7x-2-7x=2+7x-7x[/tex]

[tex]\implies 4x^2-2=2[/tex]

Add 2 to both sides:

[tex]\implies 4x^2-2+2=2+2[/tex]

[tex]\implies 4x^2=4[/tex]

Divide both sides by 4:

[tex]\implies \dfrac{4x^2}{4}=\dfrac{4}{4}[/tex]

[tex]\implies x^2=1[/tex]

Square root both sides:

[tex]\implies \sqrt{x^2}=\sqrt{1}[/tex]

[tex]\implies x= \pm 1[/tex]

Therefore, the solutions are:

[tex]x=1, \quad x=-1[/tex]

The range of the function shown on the graph above is: -10 ≤ y ≤ 3.

A range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range refers to the set of all possible output numerical values (real numbers), which are shown on the y-axis of a graph.

The vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown, the range of this graph in interval notation can be rewritten as follows:

Range = [-10, 3]

Range = -10 ≤ y ≤ 3.

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Firstly multiplication operation will be performed and the value on simplification will be -7.

The expression will be solved based on the sequence in order of operations. In the mentioned expression, parenthesis and exponents are not there. Thus, firstly we will multiply the values followed by division. Then we will perform addition and subtraction (PEMDAS).

Performing multiplication first -

Value = 27 ÷ 27 - 8

Performing division at second step -

Value = 1 - 8

We are left with subtraction, so performing it -

Value = -7

Therefore, firstly multiplication will be performed and the value is -7.

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The option that is not equivalent to the given percentage of 40% is; A:0.04.

We are given the percentage as 40%.

Now, this percentage can be rewritten as a proper fraction as;

40% = 40/100

In decimal form, this is expressed as 0.40

Now, the proper fraction 40/100 can be broken down into;

40/100 = 4/10

Further more when we divide both numerator and denominator by 2, we will get the fraction 2/5.

Thus, the only option that is not equivalent to the given percentage is option A which is 0.04.

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The correct options are;

A) 0.04

B) 0.40

C) 2/5

D) 4/10

Answer:

ASA

Step-by-step explanation:

Answer:

ASA

Step-by-step explanation:

The base of the triangle = 4(x + 1)

The Area of a triangle is given by the formula:

Substituting these expressions into the formula for the area of a triangle:

b = 4 (x + 1)

The base of the triangle = 4(x + 1)