What is the third quartile, Q3, of the following distribution?
4,5, 33, 10, 12, 14, 34, 43, 21, 22, 21, 22, 44, 29, 16, 18, 20, 24, 26, 29

Answer:

[tex]m = \frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\frac{y2 - y1}{x2 - x1}[/tex]

[tex]\frac{2-1}{3-1}[/tex]

[tex]2-1 = 1\\ 3-1=2[/tex]

[tex]m = \frac{1}{2}[/tex]

For this case we have that by definition, the slope of a line is given by:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]

We have two points through which the line passes:

[tex](x_ {1}, y_ {1}) :( 1,1)\\(x_ {2}, y_ {2}) :( 3,2)[/tex]

Substituting:

[tex]m = \frac {2-1} {3-1} = \frac {1} {2}[/tex]

Thus, the slope of the line is [tex]\frac {1} {2}[/tex]

Answer:

Option C

Answer:

Points on the Real number line correspond to Real numbers.The distance between two points is the absolute value of the difference of the corresponding numbers. ... The set of points on any line corresponds to the coordinate .

Step-by-step explanation:

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Answer:

The correct answer would be B, Sometimes.

Step-by-step explanation:

Rational numbers are sometimes the natural numbers.

Rational numbers are the numbers that can be expressed as a quotient or fraction of two integers. Rational numbers can be in the form of decimals or natural numbers. Natural Numbers are the normal integers like 1, 2, 3, 4, etc. So the resulting numbers of any equation will give a rational number or a natural number. So it is so correct to say that rational numbers are sometimes the natural numbers.  

Answer:

True

Step-by-step explanation:

The region defined by the following inequality

[tex]4x+7y<5[/tex]

is delimited by the line: [tex]4x+7y=5[/tex]

Therefore the points that are on the line that delimits the region are those where  [tex]4x+7y=5[/tex]

Since the symbol "<" represents only the values that are smaller and excludes those that are greater or equal, then the points where  [tex]4x+7y=5[/tex] are not included in the region. This is represented by drawing a dotted line

The statement is true; the border line of the inequality 4x+7y<5 is drawn as a dotted line because it does not include the boundary points as part of the solution set.

The statement that the border line of the linear inequality 4x+7y<5 is dotted is true. When graphing a linear inequality, the border line is typically solid if the inequality includes the equality (≤ or ≥), which indicates that the points on the line are included in the solution set. However, when the inequality does not include equality ( < or > without the line underneath), as in 4x+7y<5, the border line is drawn as a dotted line, signifying that points on the line are not part of the solution set. Therefore, the given statement is correct and the border line should indeed be dotted.

Answer:

The correct answer is D.

The correct identity Samuel should use is: D. (20 x 6) + (4 x 6) = 24 x 6

To find the total cost of ordering 24 lunch specials at $6.00 each, Samuel needs to compute 24×6.

The distributive property states that:

a×(b+c) = (a×b)+(a×c)

In this problem, we can break down 24 into 20 and 4, and then apply the distributive property.

This gives us:

24×6 = (20+4)×6

= (20×6) + (4×6)

Answer:

14.1 mi

Step-by-step explanation:

Use pythagorean theorem (a^2 + b^2 = c^2)

a = base

b = side

c = hypontenuse

then just plug the numbers into the formula -----> 6.3^2 + b^2 = 15.4^2

then subtract 6.3^2 from both sides ----> b^2 = 15.4^2 - 6.3^2

solve ------> b^2 = 197.47

Square root both sides and you get b = 14.1 mi as your answer  

Answer:

14.1

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

(x⁴ + x)^½

As x approaches infinity, x⁴ becomes much larger than x.  So:

(x⁴ + x)^½ ≈ (x⁴)^½ = x²

So x² grows at the same rate as (x⁴ + x)^½.

Answer:

7 laps

Step-by-step explanation:

Take the total distance and divide by the distance around the lake to determine how many laps she must run

14 km/2 km

7

She must run 7 laps

Answer:

3.86 (or 3.9)

Step-by-step explanation:

There's a logarithm function on a graphing calculator

Answer:

[tex]a_{n}[/tex] = 4n - 11

Step-by-step explanation:

These are the terms of an arithmetic sequence with n th term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

d = - 3 - (- 7) = 1 - (- 3) = 5 - 1 = 4

and a₁ = - 7, hence

[tex]a_{n}[/tex] = - 7 + 4(n - 1) = - 7 + 4n - 4 = 4n - 11

The explicit formula for the arithmetic sequence -7,-3,1,5 is an = -7 + (n-1)(4), where n is the position of the term in the sequence.

The student is asking for the explicit formula of the sequence -7,-3,1,5. This is an arithmetic sequence, where each term increases by a constant difference. The common difference (d) can be found by subtracting any term from the following term; for instance, -3 - (-7) = 4. To find the explicit formula, we'll denote the first term of the sequence as a1 which is -7. The explicit formula for an arithmetic sequence is an = a1 + (n-1)d. Substituting our values in, we get an = -7 + (n-1)(4).

Answer:

x-intercept: (1/3,0)

y-intercept: none

Answer:

-3

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Answer:

The roots of the equation 2m²+3=m are non-real roots.

Step-by-step explanation:

Given equation:

2m²+3=m

2m²-m+3=0

Here, from the equation we can obtain the following values:

a = 2, b = -1, c = 3

Discriminant of an equation is given as:

D = b²-4ac

= (-1)²-4(2)(3)

= 1 - 21

= -20

Discriminant can tell what kinds of roots the equation have.

In our case, the discriminant is less than 0.

When D < 0, the roots of the equation are complex conjugates.(non-real)

Answer:

Imaginary root

Step-by-step explanation:

-1^2-4(2*3)

1-4*6

1-24

-23

-23 has no square root or it will be a decimal.

The function that is graphed below is y = |x - 8| + 2.

Option A is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto-one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The graph of the function y = |x - 8| + 2 is a V-shaped graph with the vertex at the point (8, 2).

The function is defined as the absolute value of the difference between x and 8, plus 2.

When x is less than 8, the expression inside the absolute value bars, (x - 8), is negative, so the function becomes y = -(x - 8) + 2.

Simplifying this expression, we get y = -x + 10, which is the equation of a line with a slope of -1 and a y-intercept of 10.

This line goes downwards to the left of the vertex (8, 2).

When x is greater than 8, the expression inside the absolute value bars, (x - 8), is positive, so the function becomes y = (x - 8) + 2.

Simplifying this expression, we get y = x - 6, which is the equation of a line with a slope of 1 and a y-intercept of -6.

This line goes upwards to the right of the vertex (8, 2).

At the vertex (8, 2), the function takes the minimum value of 2.

Overall, the graph of the function y = |x - 8| + 2 is a V-shaped graph with the vertex at (8, 2), and two lines with slopes of -1 and 1 on either side of the vertex. The graph is symmetrical about the vertical line x = 8.

Thus,

The function that is graphed below is y = |x - 8| + 2.

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Step-by-step explanation:

[tex]19.60 - 3 = 16.60 \\ \frac{3}{16.60} = 0.2206 \\ 0.2206 \times 100 = 22.06\%[/tex]

Answer:

The first one: y - 2 = -5(x - 2)

Step-by-step explanation:

Answer:

the function y – 2 = –5(x – 2) is linear.

Step-by-step explanation:

We need to find the correct option from provided options which represents a linear function

Since, the linear equation is in the form of y=mx+c where m is slope of line.

In first part y – 2 = –5(x – 2)

Simplify, the function

[tex]y -2 = -5x + 10[/tex]

Add both the sides by 2, in above equation

[tex]y = -5x +12[/tex]

This function is in the form of y=mx+c

so, this is a linear function

In second part x + 7 = –4(x + 8)

Simplify, the function

[tex]x+7= -4x+32[/tex]

subtract both the sides by 7, in above expression

[tex]x= -4x+32-7[/tex]

[tex]x= -4x+25[/tex]

add both the sides by 4x,

[tex]x +4x= 25[/tex]

[tex]5x= 25[/tex]

divide both the sides by 5,

[tex]x =5[/tex]

This is not in the form of y=mx+c

so, this is not a linear function

In third part y – 3 = y(x + 4)

Simplify, the function

[tex]y-3= yx+4y[/tex]

add both the sides by 3,

[tex]y= yx+4y+3[/tex]

This is not in the form of y=mx+c

so, this is not a linear function

In fourth part y + 9 = x(x - 1)

Simplify, the function

[tex]y+9= x^{2}-x[/tex]

subtract both the sides by 9,

[tex]y= x^{2}-x-9[/tex]

This is not in the form of y=mx+c

so, this is not a linear function

Therefore, the function y – 2 = –5(x – 2) is linear.

The required inequality would be 99x + 84 ≤ 1,150. so the correct option is C.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

Given;

The cost of the shirt she bought = $ 84,

And the cost of each watch she bought = $ 99,

Now Suppose she bought x watches,

So, the cost of x watches = 99x dollars,

Also, her total spending = 84 + 99x

Since she has a total budget of $1,150,

That is her spending can not be exceed $ 1,150, ( or spending must be less than or equal to $ 1150 )

⇒ 99x + 84 ≤ 1,150

Hence the required inequality would be 99x + 84 ≤ 1,150. so the correct option is C.

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Answer:

[tex]\frac{5}{2}[/tex]

Step-by-step explanation:

recall for a line whose equation is

y = mx + b,

the slope of this line is m

the slope of a line that is perpendicular to this line is -[tex]\frac{1}{m}[/tex]

in this case,

m = -[tex]\frac{2}{5}[/tex]

hence -[tex]\frac{1}{m}[/tex]=[tex]\frac{5}{2}[/tex]

The slope of a line that is perpendicular to the line represented by the equation y = -2/5x + 4/5 is 5/2 .

The slope of a line perpendicular to a given line is equal to the negative reciprocal of the slope of the given line.

Let the given line is y = mx + c , where the slope of the line is m and the y-intercept is c .

The slope of the line perpendicular to this given line is equal to -1/m .

Given equation of line is y = -2/5x + 4/5 .

The slope of the given line is -2/5 .

Thus, the slope of the line perpendicular to this given line is equal to

= -(-5/2) = 5/2 .

Therefore, the slope of a line that is perpendicular to the line represented by the equation y = -2/5x + 4/5 is 5/2 .

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Answer:

(m-2)(m+2)

Step-by-step explanation:

a²-b²=(a-b)(a+b)

let m be a and 2 be b

m^2-2²=(m-2)(m+2)

For this case we must factor the following expression:

[tex]m ^ 2-4[/tex]

According to the formula of difference of squares we have:

[tex]a ^ 2-b ^ 2 = (a + b) (a-b)[/tex]

We have to:

[tex]a = m\\b = 2[/tex]

So, we have:

[tex]m ^ 2-4 = (m + 2) (m-2)[/tex]

Answer:

The factored expression is:[tex]m ^ 2-4 = (m + 2) (m-2)[/tex]

Multiply by 28 for the ounces

1*28= 28

3*28=84

Divide by 28 for 140

140/28= 5

Answers:

84 grams

5 ounces

Answer:

Step-by-step explanation:

Perimeter  = 60 cm

longest side = 4* shortest side (x)

longest side = 4x

shortest side = x

third (intermediate side=y= 60 -x -4x = 60-5x

The triangle inequality specifies that the sum of the two shorter sides must be greater than the longest side to form a triangle.  Hence

x + y > 4x

x + 60-5x > 4x

60 - 4x > 4x

8x < 60

x < 60/8 = 7.5, or

x < 7.5

Therefore to form a triangle, x must be less than 7.5 cm.

Now if we look at the options  both 7 and 5 are less than 7.5 cm.

40, 30 and 25 all have a problem because the longest side (4 times longer) will exceed the perimeter of 60.

Now also examine cases where 4x is not  the longest side, in which case we need

4x>=y

or

4x >= 60-5x

9x >=60

x >= 6.67

so x=5 will not qualify, because 4x will no longer be the longest side.

The only valid option is x=7 cm

The side lengths for x=7 and x=5 are, respectively,

(7, 25, 28)....

so the trapezoidal prism is really 4 rectangles and 2 isosceles trapezoids.

so we can simply get the area of each of those shapes and sum them up and that's the area of the prism.

[tex]\bf \stackrel{\stackrel{\textit{front and back}}{\textit{trapezoids}}}{2\left[ \cfrac{6(4+12)}{2} \right]}+\stackrel{\stackrel{\textit{left and right}}{\textit{rectangles}}}{2(6\cdot 6)}+\stackrel{\textit{top rectangle}}{(4\cdot 6)}+\stackrel{\textit{bottom rectangle}}{(6\cdot 12)} \\\\\\ 6(16)+72+24+72\implies 96+168\implies 264[/tex]

[tex]

f(x)=0.5(3-x) \\

f(-3)=0.5(3-(-3)) \\

f(-3)=0.5\cdot6 \\

f(-3)=3

[/tex]

Hope this helps.

r3t40

Answer:

Conclusion: x = 0

Step-by-step explanation:

given: If a ● b = 0, then a = 0 or b = 0

then for 3x = 0, either 3 = 0 (not possible because 3 is obviously not zero) or x = 0 (answer)

Answer:

A'(-2, -3)  B'(0, -3)  C'(-1, 1)

Step-by-step explanation:

change the signs for the Y coordinates because you are reflecting over the X-Axis. so 3 becomes -3, and -1 becomes 1. leave the X coordinates unchanged.

The reflection triangle ABC over the x axis is A'(–2, -3), B'(0, -3), and C'(–1, 1).

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation

If a point A(x, y) is reflected over the x axis, the new point is at A'(x, -y).

The reflection of A(–2, 3), B(0, 3), and C(–1, –1) over the x axis is A'(–2, -3), B'(0, -3), and C'(–1, 1).

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8n + 12 +(-9) -(-6n)

12 + -9 = 12-9 = 3

8n - (-6n) = 8n + 6n = 14n

The equation becomes 14n + 3

Answer:

They are complementary

Step-by-step explanation:

Complementary angles sun to 90°

∠A + ∠B = 59° + 31° = 90° ← complementary

Answer:$40.24

Step-by-step explanation:

Answer:

$40.24

Step-by-step explanation:

You just have to do $50.00 - $9.76= $40.26

Answer:

4 is the width, 14 is the length