Which graph shows the solution to the system of linear equations?

y = 2x − 2
4x − 2y = 4

Coordinate plane with one line that passes through the points 0 comma negative 2 and 1 comma 0.
Coordinate plane with one line that passes through the points 0 comma negative 1 and 1 comma 1 and another line that passes through the points 0 comma negative 2 and 1 comma 0.
Coordinate plane with one line that passes through the points 0 comma 1 and 1 comma 2.
Coordinate plane with one line that passes through the points 0 comma negative 2 and 1 comma 0 and another line that passes through the points 0 comma 1 and 1 comma 2.

After using the distribution, the value of P(X(1) < 20, X(2) > 10) is 0.18.

The distribution of random variables x(1) and X(2) have given below:

We have to determine P(X(1) < 20, X(2) > 10).

We have to determine the joint probability.

From the table we can see that the value of x(1) is less than 20 is (5, 10) and x(2) greater than the (10, 20).

P(X(1) < 20, X(2) > 10) = P(5, 10) + P(10, 20)

From the table

P(X(1) < 20, X(2) > 10) = 0.06 + 0.12

P(X(1) < 20, X(2) > 10) = 0.18

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The complete question is:

Random variables x(1) and X(2) have the following distribution:

Find P(X(1) < 20, X(2) > 10) (write up to second decimal place)

Answer:

583,200

Step-by-step explanation:

Hope it helps! =D

Answer:

583200

Step-by-step explanation:

The mean of the number of hours of sleep for this sample is 7.4, the standard deviation is 1.759186 and the variance is. 3.0947.

Standard deviation, denoted by the symbol σ, describes the square root of the mean of the squares of all the values of a series derived from the arithmetic mean which is also called the root-mean-square deviation. 0 is the smallest value of standard deviation since it cannot be negative. When the elements in a series are more isolated from the mean, then the standard deviation is also large

Mean [tex]& =\frac{\text { Sum of all data }}{\text { Total number data }} \\[/tex]

[tex]& =\frac{6+5+10+5+6+9+9+5+9+5+8+7+8+6+9+8+9+6+10+8}{20} \\& =\frac{148}{20} \\\end{aligned}$$[/tex]

= 7.4

Thus, the mean of the number of hours of sleep for the above sample is 7.4.

To find: the variance and standard deviation for the above sample.

Standard Deviation=[tex]\sqrt{\frac{\sum f_i\left(x_i-\mu\right)^2}{n-1}} \\[/tex]

[tex]& \sigma \quad=\sqrt{\left\{\begin{array}{l}(6-7.4)^2+(5-7.4)^2+(10-7.4)^2+(5-7.4)^2+(6-7.4)^2 \\+(9-7.4)^2+(9-7.4)^2+(5-7.4)^2+(9-7.4)^2+(5-7.4)^2 \\+(8-7.4)^2+(7-7.4)^2+(8-7.4)^2+(6-7.4)^2+(9-7.4)^2 \\+(8-7.4)^2+(9-7.4)^2+(6-7.4)^2+(10-7.4)^2+(8-7.4)^2\end{array}\right\}} \[/tex]

[tex]& \sigma=\sqrt{\frac{\left\{4(6-7.4)^2+4(5-7.4)^2+2(10-7.4)^2+5(9-7.4)^2+4(8-7.4)^2+(7-7.4)^2\right\}}{19}} \\& \sigma=\sqrt{\frac{\left\{4(-1.4)^2+4(-2.4)^2+2(2.6)^2+5(1.6)^2+4(0.6)^2+(-0.4)^2\right\}}{19}} \\& \sigma=\sqrt{\frac{58.8}{19}} \\& \sigma=\sqrt{3.0947} \\[/tex]

[tex]& \sigma \quad=1.759186 \\[/tex]

Variance = 3.0947

Therefore, the mean of the number of hours of sleep for this sample is 7.4, the standard deviation is 1.759186 and the variance is. 3.0947.

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The standard deviation is 71.

To find the standard deviation, first calculate the mean which is the sum of all the observations divided by the total number of observations.

Data is, 20, 40, 31, 7, 15, 29, 25, 20, 17, 32, 28, 12, 34, 29, 20, 17, 33, 23.

Total number of observations are, 18.

Sum of observations, 20+40+31+7+15+29+25+20+17+32+28+12+34+29+20+17+33+23 = 432

Mean = sum of observations/total number of observations

Mean = 432/18

Mean = 24

Standard deviation = [tex]\sigma = \sqrt{\dfrac{(\sum x_i-\mu)^2}{N}}[/tex].

Where, μ is the Mean of the observations.

N is total number of observations.

[tex]x_i[/tex]  is the ith observation.

σ = {(20-24)^2+(40-24)^2+(31-24)^2+(7-24)^2+(15-24)^2+(29-24)^2+(25-24)^2+(20-24)^2+(17-24)^2+(32-24)^2+(28-24)^2+(12-24)^2+(34-24)^2+(29-24)^2+(20-24)^2+(17-24)^2+(33-24)^2+(23-24)^2}/18

σ = {1278}/18

σ = 71

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Answer: 9,9 miles.

Step-by-step explanation: if he can run 6 miles in 51 minutes, he's running 0,11 miles per minute (calculation down below), therefore in 90 minutes he could run 9,9 miles (0,11.90).

6 mi --- 51

x ---- 1

cross multiplication,

51x = 6

x=6/51

x=0,11

If he runs 0,11 miles in 1 minute, in 90 minutes he'll do

0,11 --- 1

x ---- 90

x= 0,11 . 90

x= 9,9

The equation 2(x-3) + 21 = -3 is asking to find the value of x that makes the equation true.

Value is the worth of something in terms of the benefits, importance, or usefulness it provides. It is the relative importance or worth of something, as compared to other things. It is what people deem to be important, and it can vary depending on the individual or context. Value is not equivalent to price, which is the monetary cost of something. Value is an intangible concept and can represent the overall benefit or worth of an item, service, or experience. It can also refer to an individual’s moral or ethical standards. Value is subjective, meaning that it is based on a person’s individual beliefs and values. It is also malleable and can change over time. People can assign value to different objects, experiences, or relationships, based on what they find meaningful and important.

Distribute to get: 2x-6+21=-3

Combine like terms to get: 2x+15=-3

Solve for x: x=-21/2

Explain the problem: The equation 2(x-3) + 21 = -3 is asking to find the value of x that makes the equation true.

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Answer:

x < -2 or x > 5

Step-by-step explanation:

We want to write the compound inequality.

There is an open circle at -2 and a line going to the left.

x < -2

There is an open circle at 5 and a line going to the right.

x > 5

We use an or since they are not connected.

x < -2 or x > 5

The first investment is $22500 and second investment is $34000.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Two investments totaling $56,500 produce an annual income of $2480.

let the two investments be x and y.

So, x + y = 56500.........(1)

and, One investment yields 8 % per year, while the other yields 2 % per year then

0.08x+0.02y=2480.......(2)

Solving equation (1) and (2) we get

0.08(56500-y)+0.02y=2480

4520-0.08y+0.02*y=2480

-0.06y=-2040

y= 34000

and, x=56500-y =22500

Hence, the investments were $22500and $34000.

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Answer:

B

Step-by-step explanation:

All that they were asking for is what is given to you, so B would be right

The distance Derick walked from 12 pm to 4.45 pm is 16.625 miles

The distance is solved form the concept of speed which is defined as the ratio of distance with time

The formula for speed is

= distance covered / time taken

The time taken in the journey is

= from 12 pm to 4:45 pm = 4 hours 45 minutes = 4.75 hours

distance covered

= speed * time consumed

= 3.5 mph * 4.75 hours

= 16.625 miles

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The smaller of the triangle’s two acute angles is 65 degrees

Less than 90 degrees is the acute angle measurement. Right angles are 90 degrees in length. Angles that are obtuse are more than 90 degrees. Discover the various sorts of angles and examples of each.

Given:

Angles in a triangle

[tex]sin (4x-5)^\circ= cos (3x+4)^\cir[/tex]

Since, sin [tex]\theta[/tex]= cos(90 - [tex]\theta[/tex]),

cos(90 - (4x - 5 )) = cos(3x +4)

cos(85 - 4x) = cos (3x+4)

Cancel out the cosine functions to have:

85- 4x = 3x+ 4

81 = 7x

x= 11.57

Hence, the smaller of two acute angles is 11.57 degrees

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Answer:

27

Step-by-step explanation:

The inequalities are :

x + 31 < 1 ⇒ x < - 30 ⇒ x + 3 < -27

|x - 6| ≥ 2  ⇒x- 6 ≥ 2 and 6 - x ≤ 2

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two integers on a number line.

The occurrence of an unfair and/or uneven distribution of opportunities and resources among the people that make up a society is referred to as inequality. To different individuals and in various settings, the word "inequality" may indicate different things.

Inequality is a connection between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

The inequalities are :

x + 31 < 1 ⇒ x < - 30 ⇒ x + 3 < -27

|x - 6| ≥ 2  ⇒x- 6 ≥ 2 and 6 - x ≤ 2

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Answer:

12 feet

Step-by-step explanation:

This example can be solved using a proportion. The ratio between the height of the girl and her shadow is equal to the ratio of the height of the tree and its shadow.

Ratio of girl height to shadow length: [tex]\frac{3}{7}[/tex]

Ratio of the tree height and its shadow: [tex]\frac{x}{28}[/tex]

The proportion can be written: [tex]\frac{3}{7}=\frac{x}{28}[/tex]

The relationship between the denominators happens to be obvious, so this can be solved easily. 7 times 4 is 28, and since the ratios are equal, 3 times 4 must be X.

[tex]3\times4=12\\x=12[/tex]

The tree is 12 feet tall!

The quotient after the long division of the expression is 2x² +8x -3.

Long Division is a method for dividing large numbers, which breaks the division problem into multiple steps following a sequence. Just like the regular division problems, the dividend is divided by the divisor which gives a result known as the quotient, and sometimes it gives a remainder too.

The long division method will be done as below,

x - 3 ) 2x³ + 2x² -27x + 2( 2x² +8x -3

        -2x³ +6x²

      ________________

                8x² - 27x + 2

               -8x² +24x

     _________________

                       -3x + 2

                       3x - 9

______________________

                             -7

Hence, the quotient after the long division of the expression is 2x² +8x -3 and the remainder is -7.

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Completing the square is a strategy that is sometimes required to complete a quadratic equation, the steps and provide an example as to how it can be used are:

Writing a quadratic expression so that it contains the perfect square is known as "completing the square" in algebra. In plain English, the act of "completing the square" can be described as taking the quadratic equation "ax2 + bx + c = 0" and changing it to "a(x + p)2 + q = 0."

Example: expression is x2 - 7x.

A = 1; B = -7 when the above expression is compared to ax2 + bx + c.

The term that needs to be added, according to the formula, to convert the given expression into a perfect square trinomial is (b/2a)2 = (-7/2(1))2 = 49/4.

The term that needs to be added to make the given expression a perfect square trinomial, then, from both approaches, is 49/4.

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Answer:

The product of (-12 + 4i) and its conjugate is (-12 - 4i).

The conjugate of (-12 + 4i) is (-12 - 4i).

The stem-and-leaf plot of the given data is attached.

A stem-and-leaf plot refers to a device used to present quantitative data in a graphical format to help in visualizing the shape of a distribution. It is a table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).

From the given options, the statements that describe the percentages distributed, distribution skewness and whether there are any gaps are:

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The volume of the cone is 36π * 2√(34).

The formula for the lateral surface area of a right circular cone is:

A = π * r * l

where A is the lateral surface area, π is the constant pi, r is the radius of the base, and l is the slant height of the cone.

Given that the lateral surface area of the cone is 12√(34) * π, we can write:

[tex]12\sqrt{(34)} * \Pi = \Pi * r * l[/tex]

Dividing both sides by π and r, we can find the slant height:

l = 12√(34) / r

= 12√(34) / 6

= 2√(34) units

The volume of a right circular cone can be found using the formula:

V = (1/3) * π * r^2 * h

where V is the volume,

π is the constant pi,

r is the radius of the base, and

h is the height of the cone.

Since the cone is a right circular cone, the slant height is also the height of the cone,

So we can substitute l for h:

V = (1/3) * π * r^2 * l

= (1/3) * π * 6^2 * 2√(34)

= 36π * 2√(34)

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Answer:

Below  

Step-by-step explanation:

Here is the answer for 11pi   DEGREES

( but you may have meant 11pi RADIANS   <====but not what you posted) )

 I do not have cot function on my calculator....so I will use tan and then inverse it

 tan (11pi°) = .68876

 .68876 ^(-1) = 1.452

The simplified form of the expression (x² + 7x) / (9 - x²) is x(x + 7) / ( 3 + x )( 3 - x ).

Given the expression in the question;

(x² + 7x) / (9 - x²)

To simplify, first factor out x form x² + 7x

(x × x + 7 × x) / (9 - x²)

Factor out x

x (x + 7) / (9 - x²)

Next, simplify the denominator

x (x + 7) / (9 - x²)

Rewrite 9 as 3²

x (x + 7) / (3² - x²)

Now, since both terms are perfect squares

a² - b² = (a + b)(a - b)

Hence,

x(x + 7) / ( 3 + x )( 3 - x )

Therefore, the simplified form is x(x + 7) / ( 3 + x )( 3 - x ).

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V is a vector space with the operations of addition and scalar multiplication.

Since f(t) and g(t) are real numbers, you're utilizing the fact that the real numbers themselves are commutative in that step, which truly confused me when I first learned about it and after.

Let V denote the set of all differentiable real-valued functions defined on the real line.

You only need to mention that real-number addition is commutative. Since f is not a number until you evaluate, you couldn't do it before you did.

On a different note, you cannot say that

f+g=f(t)+g(t)

but you can say that (f+g)(t)=f(t)+g(t)

So  V is a vector space with the operations of addition and scalar multiplication.

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True statements about the procedure implement a linear search, So the correct option is, ii only.

Linear search, also known as sequential search, is a simple search algorithm that iterates through an array or a list of elements one by one, starting from the first element, until the desired element is found.

The basic steps of linear search are:

The time complexity of the linear search is O(n), where n is the number of elements in the array/list.

This means that the algorithm takes n steps in the worst-case scenario to find the desired element in an array/list of n elements. Linear search is generally less efficient than other search algorithms like binary search for large data sets.

Linear search can be used on unsorted arrays/lists as well as on sorted arrays/lists. It is a simple and easy-to-implement algorithm and is suitable for small data sets or when the data is not sorted and the data changes frequently.

In addition, a linear search algorithm can also be used to find the index of the element in the array/list if the element is found.

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Population: The customers of Jerry's Barbershop. Time is taken to cut hair: Minutes. Amount of money spent: Currency (e.g. dollars).

Stage of life: Categorical (Child, Teen, or Adult)

A population is a discrete group of people, animals, or things that can be recognized by at least one common trait for the purposes of data collection and analysis in statistics and other fields of mathematics.

As per the given information, the required solution would be as:

Population: The customers of Jerry's Barbershop.

Variables and their units are, as follows:

Time taken to cut hair: Minutes

Amount of money spent: Currency (e.g. dollars)

Stage of life: Categorical (Child, Teen, or Adult)

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Answer:

Step-by-step explanation:

A = B⋅H/2

Base = 10 m

Height = 12m

10⋅12= 120

120/2=60²

Answer:

3 * 8 = 42, divide that by 38, then put it inside the cool looking v sign, and that will give you 89 weed leaves left as trim. Take the 21 add that with the divisor of the previous problem, then you get 25 PLUS the breadsticks, and you get 96. Last step is 96 - 29 = how much bud is left to smoke!

Hope this helped!  

Answer:

x = -3 & 3

Step-by-step explanation:

∣5xI = 15

divide both sides by 5:

(∣5xI)/5 = 15/5

∣xI = 3

I-3I = 3 AND I3I = 3

so:

x = -3 & 3

The sum of the given geometric series is given by 79545.8567

Any progression in which the ratio of adjacent terms is fixed is a Geometric Progression. The general form of representation of a geometric sequence is a, ar, ar², ar³,.....

Given here: The expression  1000(1.02)³⁰+ 1000(1.05)(1.02)²⁹+ 1000(1.05)²(1.02)²⁸ + ......

Clearly we can observe that the given sum is a geometric progression with common ratio =1.05/1.02

The given sum is a sum of first 29 terms of the G.P

Thus Sₙ = a(rⁿ - 1) / (r - 1)

        S₂₉=1000×1.02³⁰(1.029²⁹-1) /1.0294-1

              =1811.36(2.291106-1)/0.0294

              =1811.36(1.2911)/0.0294

              =79545.8567

Hence, The sum of the given geometric series is given by 79545.8567

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Answer:

Step-by-step explanation