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Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system?

A coordinate plane linear graph on inequalities.

Applying the definition of the median of a triangle, the length of AO is calculated as: 14 units.

The median of a triangle is a line segment that joins the midpoint of a side of a triangle and the opposite vertex to the side.

There are three medians in a triangle, and the three of them intersect at a point inside the triangle. This point of intersection is known as the centroid.

According to the centroid theorem of a triangle, the length from the vertex to the centroid is two-third of the length of a median.

Thus, the figure shows that triangle ABC has three medians, BL, AM, and CK, which intersect at point O. This means the centroid of the triangle is point O.

By implication, it means that:

Length of AO = 2/3 * (length of AM)

Plug in the value of AM:

Length of AO = 2/3 * (21) [centroid theorem]

AO = 2 * 7

AO = 14

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To determine whether the system of equations is consistent and independent, consistent and dependent, or inconsistent, we need to first solve the system of equations to find the value of x and y that satisfy both equations.

To solve the system of equations, we can first solve the first equation for y:

y = −3x + 1

Next, we can substitute this expression for y into the second equation and solve for x:

2y = −6x + 2

2 * (−3x + 1) = −6x + 2

−6x + 2 = −6x + 2

0 = 0

Since the two equations are equivalent, the system of equations is consistent and dependent, meaning that there is only one possible solution (x = 0, y = 1) that satisfies both equations.

fractions with the same denominator added together

You must add the numerators and keep the same denominator when adding fractions with the same denominator. Since the denominators of the two fractions are the same, we must add the numerators while maintaining the same denominator, which is 4.

What are the parts of fraction?

A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line.

The number below the bar is called the denominator . It tells the number of equal parts into which the whole has been divided. The number above the bar is called the numerator. It tells how many of the equal parts are being considered.

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The variables x, y, z associated to the parallelogram are equal to 60, respectively.

A parallelogram is a quadrillateral formed by two pairs of parallel sides. The figure shows a parallelogram since the following relationships are met: BC ║ AD, AB ║ CD. We need three equations to determine the values of x, y and z and this can be obtained by means of parallelogram properties:

y = x

y + (x + y) = 180°

z + (x + y) = 180°

First, substitute x on the second and third equations:

3 · y = 180°

z + 2 · y = 180°

Second, find y:

y = 180° / 3

y = 60

Third, find z:

z = 180° - 2 · y

z = 180° - 2 · 60

z = 180° - 120°

z = 60

Fourth, find x:

x = 60

The values of variables x, y, z are 60, respectively.

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(a) Is this an observational study or an experiment?

ans=Observational study – no treatment was imposed

(b) What are the explanatory and response variables?

ans=explanatory – time spent in child care from birth to age 4 response – adult rating of children’s behavior

d) Does this study show that child care causes children to be more aggressive? Explain.

No. Observational studies cannot show cause-and-effect

Researchers=someone whose job is to study a subject carefully, especially in order to discover new information or understand the subject better: She is a leading researcher in the field.

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If the first bus is boarded at a rate of 15 people per minute, the domain of the function is; (15 ≤ x ≤ 45)

We are told that;

Total number of Juniors at Smithers High School that are taking a class trip = 130

Number of buses taking each student to their destination = 3 buses

Capacity of each bus = 45 people

Now, if the function  f(x) describes the total number of people on the first

bus, where x is the number of minutes spent loading the bus.

Then since the maximum number of people on the first bus is 45, then it means that the domain of the function is;

(15 ≤ x ≤ 45)

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Answer: 1/20

Step-by-step explanation:

....................................

The population proportion of non-fatal accidents that involved the use of a cell phone is 0.03567

A population proportion is known as the share of a population that belongs to a particular group. The Confidence intervals are used to estimate population proportions.

as per given in the question,

The total number of accidents (n) are 600

The accidents involving cell phones (x) are 214

the sample proportion ([tex]\hat p[/tex]) = x/n

where

x is the count of the successes

n is the total size of the population

P is the population proportion

=> 214/600

=> 0.3567

the estimated point for population proportion is

[tex]\hat p[/tex] = 0.03567

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Answer:

D

Step-by-step explanation:

To solve for a you would need to subtract k from both sides.  That would leave you with

y - k = a ([tex]x-h)^{2}[/tex]  then, divide both sides by [tex](x-h)^{2}[/tex] to get letter d

Answer:

.......................

Answer:

$22,950,  $4,590

Step-by-step explanation:

Divide 306,000 by 100. This equals 3060, or one percent of the profit.

Multiply this profit by 7.5 to get $22,950, which is the amount to agency makes.

To find what the agent makes, divide 22,950 by 10 to get 2,295, or ten percent of the agency's profits. Double it and it will 20 percent or $4,590, the amount the agent makes.

Answer: $48.00

Step-by-step explanation:

His membership was $25.00

And EACH time he comes he pays $5.75.

so your equation is 25.00 + (5.75 x 4) = $48.00

The position of mailbox after 10s is equal to sum displacements is 14m.

The principle is that the slope of the line on a velocity-time graph reveals useful information about the acceleration of the object. If the acceleration is zero, then the slope is zero (i.e., a horizontal line). If the acceleration is positive, then the slope is positive (i.e., an upward sloping line).

Given velocity time graph understand in three parts.

1. first 6s mailbox have constant velocity 3m/s

the displacement covered by it = area under v-t graph(square shape)

s1=3 x 6 =18m

2. the mailbox at rest at 6-8 s.

the displacement covered by it s2=0

3. the mail returned with constant velocity 2m/s

Displacement is defined to be the change in position of an object. It can be defined mathematically with the following equation:

Displacement=Δx=[tex]x_{f} - x_{0}[/tex]

[tex]x_{f}[/tex]=refers to the value of the final position.

[tex]x_{0}[/tex]= refers to the value of the initial position.

Δx is the symbol used to represent displacement

the displacement covered by it s3 =(10-8) (-2) =-4m

the position of mailbox after 10s is equal to sum displacements=s1+s2+s3 =18+0-4=14m the displacement - time graph.

Therefore, the position of mailbox after 10s is equal to sum displacements is 14m.

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Draw the mail carrier's position-versus-time graph. Assume that x=0m at t=0s

What is the position of the mailbox?

[tex]|3x+4|-9=0[/tex]

Add 9 to both sides:

[tex]|3x+4|-9+9=0+9[/tex]

[tex]|3x+4|=9[/tex]

Solve the Absolute Value:

[tex]3x+4=9or3x+4=-9[/tex]

__________________________________________________________

[tex]3x+4=9[/tex]

Subtract 4 from both sides:

[tex]3x+4-4=9-4[/tex]

[tex]3x=5[/tex]

Divide both sides by 3:

[tex]\dfrac{3x}{3} =\dfrac{5}{3}[/tex]

[tex]\fbox{x = $\dfrac{5}{3} $ or 1$\dfrac{2}{3}$}[/tex]

__________________________________________________________

[tex]3x+4=-9[/tex]

Subtract 4 from both sides:

[tex]3x+4-4=-9-4[/tex]

[tex]3x=-13[/tex]

Divide both sides by 3:

[tex]\dfrac{3x}{3} =\dfrac{-13}{3}[/tex]

[tex]\fbox{x = $\dfrac{13}{3} $ or -4$\dfrac{1}{3} $}[/tex]

________________________________________________________

[tex]\fbox{Options A and D}[/tex]

Answer: 22.5g+(22.5g-7.5g)

Step-by-step explanation: Its because its all the information combined.

With the mentioned area of fabric, the five person in group will get 6.47 ft² of fabric per person.

Firstly converting the area of fabric from mixed fraction to fraction.

The area of fabric = (32×3 + 1)/3

Performing multiplication and addition on Right Hand Side of the equation

The area of fabric = 97/3 ft²

Amount of fabric each person gets = (97/3)/5

Performing division on Right Hand Side of the equation

Amount of fabric each person gets = 97/(3×5)

Amount of fabric each person gets = 97/15

Amount of fabric each person gets = 6.47 ft²

Thus, each person will get the fabric of area 6.47 ft².

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The result of the multiplication of  (√2x³ +√12x)(2√10x³ + √6x²) is

[tex]2\sqrt{20}x^6 + \sqrt{12}x^5 + 2\sqrt{120}x^4 + \sqrt{72}x^3[/tex]

What is multiplication?

Multiplication is a mathematical operation in which one number is multiplied by another. It is usually used to calculate the product of two or more numbers. It is an important operation in mathematics and is used in a variety of ways, including calculating the area of a rectangle, the volume of a cube, and the total cost of items purchased at a store. Multiplication is often represented by the multiplication symbol, which is usually an 'x' or an asterisk (*). When two numbers are multiplied, the result is called the product. For example, if two numbers are multiplied together, the product is the answer to the question "what is the result of multiplying these two numbers together?" The answer is the product of the two numbers.

Here the multiplication given is

(√2x³ +√12x)(2√10x³ + √6x²)

[tex]2\sqrt{20}x^6 + \sqrt{12}x^5 + 2\sqrt{120}x^4 + \sqrt{72}x^3[/tex]

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The correct statements are; function g is positive over (-∞, ∞), function g has a y-intercept of (0,4) and function g decreasing over the interval (-∞, 0)

A function is defined as a relation between a set of inputs having one output each.

Given that, function g is a transformation of the parent exponential function and the domain of function g is x > 0

Studying the graph, we can conclude that,

function g is positive over (-∞, ∞)

function g has a y-intercept of (0,4)

function g decreasing over the interval (-∞, 0)

Hence, The correct statements are; function g is positive over (-∞, ∞), function g has a y-intercept of (0,4) and function g decreasing over the interval (-∞, 0)

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The vector function that represents the space curve of intersection of the ellipsoid and the plane is given by[tex]$\mathbf{r}(t) = (x(t), y(t), z(t))$[/tex] and [tex]x(t) = a\cos(t)$ y(t) = b\sin(t)$ $z(t) = \frac{-d - ax(t) - by(t)}{c}$$[/tex]

Let [tex]$\mathbf{x} = (x, y, z)$[/tex] be the position vector of a point on the ellipsoid, and [tex]$a, b, c$[/tex] be the corresponding semi-major axes. Then the equation is

[tex]$$\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1.$$[/tex]

The equation of the plane is

[tex]$$ax + by + cz + d = 0.$$[/tex]

The vector function that represents the space curve of intersection of the ellipsoid and the plane is given by

[tex]$$\mathbf{r}(t) = (x(t), y(t), z(t)),$$[/tex]

where

[tex]$$x(t) = a\cos(t)$$$$y(t) = b\sin(t)$$$$z(t) = \frac{-d - ax(t) - by(t)}{c}$$[/tex]

The vector function that represents the space curve of intersection of the ellipsoid and the plane is given by [tex]$\mathbf{r}(t) = (x(t), y(t), z(t))$[/tex]where [tex]$x(t)$[/tex]and [tex]$y(t)$[/tex] are the coordinates of points on the ellipsoid, and [tex]$z(t)$[/tex] is determined by the equation of the plane. The vector function allows us to represent the intersection of the ellipsoid and the plane as a space curve.

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Answer: B

Step-by-step explanation:

The constant rate of change or slope is rise/run

Let's pick 2 points ( 4, 12) ( 10, 0)

We see that the y decreases by 12 and the x increase by 6, so our slope is

-12/6 = -2 hours per person

So the answer is B

Increasing, as the slope is positive (1/2)

Answer:

Increasing.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Given linear equation:

[tex]y=\dfrac{1}{2}x+2[/tex]

Comparing the given linear equation with the slope-intercept formula, the slope of the given equation is ¹/₂.

The graph of a linear equation is increasing if its slope is positive.

(y-values increase as x-values increase).

The graph of a linear equation is decreasing if its slope is negative.

(y-values decrease as x-values increase).

Therefore, as the slope of the given linear equation is positive, its graph is increasing.

Answer:

x = 145°

Step-by-step explanation:

x and 35° are a linear pair and sum to 180° , then

x + 35° = 180° ( subtract 35° from both sides )

x = 145°

The word IRON can be arranged is 24 unique ways.

Given:

The word = IRON

The number of unique ways in which the letters in the word IRON can be arranged = ?

The number of letters in IRON = 4

The number of positions = 4

In the first position, any one of the 4 letters can be placed

In the second position any one of the remaining 3 letters can be placed

In the third position any one of the remaining 2 letters can be placed

The fourth position can be filled with the left over letter

So the total number arrangement in unique way

= (Number of ways to fill in 1st position)* (Number of ways to fill in 2nd position)* (Number of ways to fill in 3rd position)* (Number of ways to fill in 4th position)

=> 4 *3*2*1

= 24 ways

Hence, The word IRON can be arranged is 24 unique ways.

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The factor which tarriq musr use if solving the equation using the multiplication property of equality to finish solving is 2.

The correct answer option is option D

Tarriq solution:

50 + 2x = –190

50 + 2x = –190

50 – 50 + 2x = –190 – 50

2x = –240

Correct solution:

50 + 2x = –190

Subtract 50 from both sides

50 - 50 + 2x = -190 - 50

2x = - 240

divide both sides by 2

x = -240/2

x = -120

In conclusion, x = -120 is the solution to tarriq equation if using multiplication property of equality.

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Answer:

8) y = 4

9) y = x

Step-by-step explanation:

8) Parallel = Same slope

y = mx + b

m = 0

4 = - 4(0) + b

4 = b

y = 4

9) y = x + b

7 = 7 + b

b = 0

The answer to 2 to the power of three halves equal to? is square root of 8 cube root of 8 cube root of 16 square root of 16 is  [tex]\sqrt{8}[/tex]

In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4² = ² = 16.

From the question, we can simplify the question as

[tex]2^{\frac{3}{2} }[/tex]

simplifying further by simplifying the power

[tex]2^{\frac{3}{2} }[/tex] = [tex](2^{3})\frac{1}{2}[/tex]

= [tex]\sqrt{2^{3} }[/tex]

= [tex]\sqrt{8}[/tex]

hence, the solution to the problem is [tex]\sqrt{8}[/tex]

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Answer:

720 / 6 = 120

120 * 4 = 480

P(1) = 120/720

P(2) = 120/720

P(3) = 120/720

P(4) = 120/720

P(5) = 120/720

P(6) = 120/720

P(1 + 2 + 3 + 4) = 480/720

Step-by-step explanation:

The difference between the interest compounded daily and the interest compounded annually is $67.13.

To calculate the interest earned by your money annually, you calculate as follows;

To determine the interest, use FV - amount invested

FV = P (1 + r)^n

the above represents,

FV = Future value

P = Present value

R = interest rate

N = number of years

$25,000 (1.0725) = 26,812.50

26,812.50 - $25,000 = $1,812.50

What is the interest earned in your money is compounded on a daily basis?

$25,000x (1 + 0.0725 /365)^365 = 26,879.63

26,879.63 - $25,000 = $1879.63

What is the difference in interest?

$1879.63 -  $1,812.50 = $67.13

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Answer:

[tex] r = \sqrt{\dfrac{V}{\pi h}} [/tex]

Step-by-step explanation:

V = πr²h

Switch sides.

πr²h = V

Divide both sides by πh.

r² = V/(πh)

Take the square root of both sides.

r = √[V/(πh)]

[tex] r = \sqrt{\dfrac{V}{\pi h}} [/tex]

64 observations were randomly selected at random from a population of 500. the population standard deviation is 16.The standard deviation of the sample mean is 4 (16/√64).

The standard deviation of the sample mean is calculated by dividing the population standard deviation (16) by the square root of the sample size (64).

Consequently, the sample mean's standard deviation is

16/√64 = 4.

This means that the expected spread of the sample means is 4, which is less than the population standard deviation of 16. This is because the sample is smaller than the population, so the sample standard deviation will be smaller than the population standard deviation.

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